Digital counting of individual molecules by stochastic attachment of diverse label-tags

ABSTRACT

Compositions, methods and kits are disclosed for high-sensitivity counting of individual molecules by stochastic labeling of a identical molecules in mixtures of molecules by attachment of a unique label-tags from a diverse pool of label tags to confer uniqueness to otherwise identical or indistinguishable events. Individual occurrences of target molecules randomly choose from a non-depleting reservoir of diverse label-tags. Labeled molecules may be detected by hybridization or sequencing based methods. Molecules that would otherwise be identical in information content are labeled to create a separately detectable product that can be distinctly detected. The disclosed stochastic transformation methods reduce the problem of counting molecules from one of locating and identifying identical molecules to a series of binary digital questions detecting whether preprogrammed label-tags are present. The methods may be used, for example, to count a given species of molecule within a sample.

RELATED APPLICATIONS

This application claims priority to U.S. Provisional Application No. 61/286,768 filed Dec. 15, 2009, and is a continuation-in-part of U.S. application Ser. No. 12/969,581, filed Dec. 15, 2010, the contents of which are incorporated herein in their entireties.

STATEMENT AS TO FEDERALLY SPONSORED RESEARCH

This invention was made with the support of the United States Government under Contract Number 1 R43 HG007130 by THE NATIONAL INSTITUTES OF HEALTH.

SEQUENCE LISTING

The instant application contains a Sequence Listing which has been submitted in ASCII format via EFS-Web and is hereby incorporated by reference in its entirety. Said ASCII copy, created on Jul. 31, 2014, is named 41977-701.501_SL.txt and is 399 Kilobytes in size.

FIELD OF THE INVENTION

Methods, compositions and products for counting individual molecules by stochastic attachment of diverse label-tags from a set of label-tags, followed by amplification and detection are disclosed.

BACKGROUND OF THE INVENTION

Many processes are characterized or regulated by the absolute or relative amounts of a plurality of items. For example, in biology, the level of expression of particular genes or groups of genes or the number of copies of chromosomal regions can be used to characterize the status of a cell or tissue. Analog methods such as microarray hybridization methods and real-time PCR are alternatives, but digital readout methods such as those disclosed herein have advantages over analog methods. Methods for estimating the abundance or relative abundance of genetic material having increased accuracy of counting would be beneficial.

The availability of convenient and efficient methods for the accurate identification of genetic variation and expression patterns among large sets of genes may be applied to understanding the relationship between an organism's genetic make-up and the state of its health or disease, Collins et al, Science, 282: 682-689 (1998). In this regard, techniques have been developed for the analysis of large populations of polynucleotides based either on specific hybridization of probes to microarrays, e.g. Lockhart et al. Hacia et al, Nature Genetics, 21: 4247 (1999), or on the counting of tags or signatures of DNA fragments, e.g. Velculescu et al, Science, 270: 484-487 (1995); Brenner et al, Nature Biotechnology, 18: 630-634 (2000). These techniques have been used in discovery research to identify subsets of genes that have coordinated patterns of expression under a variety of circumstances or that are correlated with, and predictive of events, of interest, such as toxicity, drug responsiveness, risk of relapse, and the like, e.g. Golub et al, Science, 286: 531-537 (1999); Alizadeh et al, Nature, 403: 503-511 (2000); Perou et al, Nature, 406: 747-752 (2000); Shipp et al, Nature Medicine, 8: 68-74 (2002); Hakak et al, Proc. Natl. Acad. Sci., 98: 47454751 (2001); Thomas et al, Mol. Pharmacol., 60: 1189-1194 (2001); De Primo et al, BMC Cancer 2003, 3:3. Not infrequently the subset of genes found to be relevant has a size in the range of from ten or under to a few hundred.

In addition to gene expression, techniques have also been developed to measure genome-wide variation in gene copy number. For example, in the field of oncology, there is interest in measuring genome-wide copy number variation of local regions that characterize many cancers and that may have diagnostic or prognostic implications. For a review see Zhang et al. Annu. Rev. Genomics Hum. Genet. 2009. 10:451-81.

While such hybridization-based techniques offer the advantages of scale and the capability of detecting a wide range of gene expression or copy number levels, such measurements may be subject to variability relating to probe hybridization differences and cross-reactivity, element-to-element differences within microarrays, and microarray-to-microarray differences, Audic and Claverie, Genomic Res., 7: 986-995 (1997); Wittes and Friedman, J. Natl. Cancer Inst. 91: 400-401 (1999).

On the other hand, techniques that provide digital representations of abundance, such as SAGE (Velculescu et al. Science 270, 484-487 (1995) and Velculescu et al. Cell 88 (1997) or MPSS (Brenner et al, cited above), are statistically more robust; they do not require repetition or standardization of counting experiments as counting statistics are well-modeled by the Poisson distribution, and the precision and accuracy of relative abundance measurements may be increased by increasing the size of the sample of tags or signatures counted, e.g. Audic and Claverie (cited above). SAGE relies on short sequence tags (10-14 bp) within transcripts as an indicator of the presence of a given transcript. The tags are separated from the rest of the RNA and can be linked together to form long serial molecules that can be cloned and sequenced. Quantitation of the number of times a particular tag is observed provides an estimate of the relative expression level of the corresponding transcript, relative to other tagged transcripts, but not an actual count of the number of times that transcript appears. Other methods based on estimating relative abundance have also been described. See, for example, Wang et al. Nat. Rev. Genet. 10, 57-63 (2009).

Both digital and non-digital hybridization-based assays have been implemented using oligonucleotide tags that are hybridized to their complements, typically as part of a detection or signal generation schemes that may include solid phase supports, such as microarrays, microbeads, or the like, e.g. Brenner et al, Proc. Natl. Acad. Sci., 97: 1665-1670 (2000); Church et al, Science, 240: 185-188 (1988); Chee, Nucleic Acids Research, 19: 3301-3305 (1991); Shoemaker et al., Nature Genetics, 14: 450456 (1996); Wallace, U.S. Pat. No. 5,981,179; Gerry et al, J. Mol. Biol., 292: 251-262 (1999); Fan et al., Genome Research, 10: 853-860 (2000); Ye et al., Human Mutation, 17: 305-316 (2001); and the like. Bacterial transcript imaging by hybridization of total RNA to nucleic acid arrays may be conducted as described in Saizieu et al., Nature Biotechnology, 16:45-48 (1998). Accessing genetic information using high density DNA arrays is further described in Chee et al., Science 274:610-614 (1996). Additional methods for digital profiling are disclosed, for example, in U.S. Patent Pub. 20050250147 and U.S. Pat. No. 7,537,897. Tagging approaches have also been used in combination with next-generation sequencing methods, see for example, Smith et al. NAR (May 11, 2010), 1-7.

A common feature among all of these approaches is a one-to-one correspondence between probe sequences and oligonucleotide tag sequences. That is, the oligonucleotide tags have been employed as probe surrogates for their favorable hybridizations properties, particularly under multiplex assay conditions.

Determining small numbers of biological molecules and their changes is essential when unraveling mechanisms of cellular response, differentiation or signal transduction, and in performing a wide variety of clinical measurements. Although many analytical methods have been developed to measure the relative abundance of different molecules through sampling (e.g., microarrays and sequencing), few techniques are available to determine the absolute number of molecules in a sample. This can be an important goal, for example in single cell measurements of copy number or stochastic gene expression, and is especially challenging when the number of molecules of interest is low in a background of many other species. As an example, measuring the relative copy number or expression level of a gene across a wide number of genes can currently be performed using PCR, hybridization to a microarray or by direct sequence counting. PCR and microarray analysis rely on the specificity of hybridization to identify the target of interest for amplification or capture respectively, then yield an analog signal proportional to the original number of molecules. A major advantage of these approaches is in the use of hybridization to isolate the specific molecules of interest within the background of many other molecules, generating specificity for the readout or detection step. The disadvantage is that the readout signal to noise is proportional to all molecules (specific and non-specific) specified by selective amplification or hybridization. The situation is reversed for sequence counting. No intended sequence specificity is imposed in the sequence capture step, and all molecules are sequenced. The major advantage is that the detection step simply yields a digital list of those sequences found, and since there is no specificity in the isolation step, all sequences must be analyzed at a sufficient statistical depth in order to learn about a specific sequence. Although significant technical advances in sequencing speed and throughput have occurred, the statistical requirements imposed to accurately measure small changes in concentration of a specific gene (or target) or a few targets within the background of many other sequences requires measuring many sequences that are not of interest to find the ones that are of interest. Each of these techniques, PCR, array hybridization and sequence counting is a comparative technique in that they primarily measure relative abundance, and do not typically yield an absolute number of molecules in a solution. Digital PCR is one method that may be used for absolute counting of nucleic acids (B. Vogelstein, K. W. Kinzler, Proc Natl Acad Sci USA 96, 9236 (Aug. 3, 1999). In this application of PCR solutions are progressively diluted into individual compartments until there is an average probability of one molecule per two wells, then detected by PCR. Although digital PCR can be used as a measure of absolute abundance, the dilutions must be customized for each type of molecule, and thus in practice the method is generally limited to the analysis of a small number of different molecules.

SUMMARY OF THE INVENTION

High-sensitivity single molecule digital counting by the stochastic labeling of a collection of identical molecules is disclosed. Each copy of a molecule randomly chooses from a non-depleting reservoir of diverse label-tags. The uniqueness of each labeled molecule is determined by the statistics of random choice, and depends on the number of copies of identical molecules in the collection compared to the diversity of label-tags. The size of the resulting set of labeled molecules is determined by the stochastic nature of the labeling process, and analysis reveals the original number of molecules. When the number of copies of a molecule to the diversity of label-tags is low, the labeled molecules are highly unique, and the digital counting efficiency is high. This stochastic transformation relaxes the problem of counting molecules from one of locating and identifying identical molecules to a series of yes/no digital questions detecting whether preprogrammed label-tags are present. The conceptual framework for stochastic mapping of a variety of molecule types is developed and the utility of the methods are demonstrated by stochastically labeling 360,000 different fragments of the human genome. The labeled fragments for a target molecule of choice are detected with high specificity using a microarray readout system, and with DNA sequencing. The results are consistent with a stochastic process, and yield highly precise relative and absolute counting statistics of selected molecules within a vast background of other molecules.

The methods disclosed herein for digital counting of individual molecules may be applied to a single target or to a plurality of different targets simultaneously. In preferred embodiments the targets are nucleic acids, but may be a variety of biological or non-biological elements. Targets are labeled so that individual occurrences of the same target are marked by attachment of a different label-tag to difference occurrences. The attachment of the label-tag confers a separate, determinable identity to each occurrence of targets that may otherwise be indistinguishable. Preferably the label-tags are different sequences that tag or mark each target occurrence uniquely. The resulting modified target comprises the target sequence and the unique label-tag identifier (which also may be referred to herein as label-tag, counter, or identifier). The junction of the target and identifier forms a uniquely detectable mechanism for counting the occurrence of that copy of the target. The attachment of the identifier to each occurrence of the target is a random sampling event. Each occurrence of target could choose any of the identifiers from a pool of identifiers. Each identifier is present in multiple copies so selection of one copy does not remove that identifier sequence from the pool of identifiers so it is possible that the same identifier will be selected twice. The probability of that depends on the number of target occurrences relative to the number of different identifier sequences.

Each stochastic attachment event, where a target occurrence is attached to a unique identifier, results in the creation of a novel sequence formed at the junction of the identifier and the target. For a given target, the resulting products will contain the same target portion, but each will contain a different identifier sequence (T1L1, T1L2, . . . T1LN where N is the number of different occurrences of target1, “T1” and L is the identifier, L1, L2 . . . LN). In preferred aspects the occurrences are detected by hybridization. In some aspects the methods and systems include a probe array comprising features, wherein each feature has a different combination of target sequence with identifiers, 1 to N wherein N is the number of unique identifiers in the pool of identifiers. The array has N features for each target, so if, for example, there are 8 targets to be analyzed there are 8 times N features on the array to interrogate the 8 targets.

In some aspects methods and kits for counting the number of occurrences of a two or more different species of target nucleic in a complex mixture of target and non-target species are disclosed. The steps may include covalently or non-covalently attaching a label-tag from a pool of label-tags to individual occurrences of the each of the target nucleic acid species of interest to form sets of targets that are distinctly labeled within species so that instead of many undistinguishable molecules of each species there are many distinguishable molecules of each species. The species are distinguishable from one another on the basis of differences between species. The label-tag are selected from a pool for attaching in an approximately random manner and preferably at least 90% of the labeled targets within a species have a label-tag that is different from all other labeled targets in that species. The number of different molecules of a given species is then approximately (within the counting error of the system) equal to the number of different label-tags that are counted. In many aspects the label-tag-targets can be amplified prior to detection.

Methods of detection include hybridization based methods and sequencing based methods. Other methods such as size separation, mass spec or optical scanning methods may also be used. They nature of the label-tags will guide the detection mechanism.

Attachment of the label-tags may be by any means available. In preferred aspects where the targets are biological molecules such as nucleic acids or proteins the labels are preferably oligonucleotides or peptides. Methods for attaching oligonucleotide or nucleic acid sequences to nucleic acids may include ligation, polymerization and primer mediated extension reactions, for example.

Kits for labeling targets within mixtures and for amplification and detection of the label-tag-targets are also disclosed. Kits may include materials or reagents for carrying out a method of the invention and may include systems that allow for the storage, transport, or delivery of reaction reagents (e.g., probes, enzymes, etc. in the appropriate containers) and/or supporting materials (e.g., buffers, written instructions for performing the assay etc.) from one location to another. For example, kits include one or more enclosures (e.g., boxes) containing the relevant reaction reagents and/or supporting materials for assays of the invention. In one aspect, kits of the invention comprises pools of label-tags, pools of label-tag containing primers or pools of label-tag containing adaptors. Enzymes that may be included in the disclosed kits include a ligase, a terminal transferase, RNaseH, reverse transcriptase, flap endonuclease, DNA polymerase, and restriction enzymes.

It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate several exemplary embodiments of the disclosure and together with the description, serve to explain certain teachings.

BRIEF DESCRIPTION OF THE DRAWINGS

The skilled artisan will understand that the drawings described below are for illustration purposes only. The drawings are not intended to limit the scope of the present teachings in any way.

FIG. 1 shows a schematic of labeling target molecules with a pool of label-tags.

FIG. 2A shows a schematic of detection of labeled targets on an array having features that are label-tag specific and target specific.

FIG. 2B shows a schematic of detection of several different targets by hybridization to an array having features containing support bound probes that are specific for junctions between label-tags and each of three different target species to facilitate counting of targets.

FIG. 2C shows a schematic for detection of individual label-target combinations by label-specific and target directed PCR.

FIG. 3 shows a schematic of a method for circularizing targets and amplifying with gene specific primers followed by detection of the target-label-tag junction.

FIG. 4 provides an example of a genomic target ligated at either end to a label-tag adaptor.

FIG. 5 shows a schematic of a method for target preparation wherein the label-tags are ligated to the targets as part of adaptors that have common priming sequences to facilitate amplification.

FIG. 6 shows a method for stochastic counting by fragmentation where the unique end of the fragment is the label-tag used for counting.

FIG. 7 shows a schematic of a method for detection of ligation products by hybridization to array probes that are complementary to the sequence resulting from the ligation.

FIG. 8 shows a schematic of the arrangement and position of the adaptors, PCR primers, and the biotinylated array-ligation probe in one exemplary sample prep method.

FIG. 9 is a schematic of a method for using ligation based read out on arrays to detect labeled targets and minimize partial target hybridization.

FIG. 10 shows the arrangement of the adaptors, label-tags and primers used to convert the labeled sample into sequencing template.

FIG. 11 is a plot of the number of label-tags from a non-depleting reservoir of 960 label-tags that are predicted to be captured at least once, exactly once or exactly twice.

FIG. 12 is a plot of counting results for 4 different DNA copy number titrations using microarray hybridization (on left) or DNA sequencing (on right).

FIG. 13 shows relative copy ratios of three tested gene targets representing copy number 1, 2 or 3 at different dilutions as analyzed using the disclosed methods.

FIG. 14 shows a comparison between experimentally observed label-tag usage and predicted label-tag usage from stochastic modeling.

FIG. 15 shows a plot of the expected label-tag usage (y-axis) when ligating to a given number of target molecules (x-axis).

FIG. 16 shows a plot of number of target molecules (x-axis) compared to counting efficiency (y-axis). The nset is a blow-up of the upper left region of the graph.

FIG. 17 shows a schematic of a method for attaching label-tags to targets using a splint having a variable region.

FIG. 18 shows a schematic of a method for enriching for molecules that contain label-tags, target or both.

FIG. 19 is a plot of the intensity observed compared to the number of fragments when fragments are binned according to size.

FIG. 20 shows label-tags observed by microarray hybridization plotted against intensity (y-axis) for each of 960 label-tags for the chromosome 4 gene target.

FIG. 21 shows frequency plots (y-axis, log-scale) of intensity distributions of the 960 label-tags in the microarray experiments with the counting threshold applied indicated by the dashed line.

FIG. 22 shows a simulated PCR run showing the replication outcome for 500 molecules of a target fragment ligated to a library of 960 label-tag counters.

FIG. 23 shows intensities of 1,152 array probes associated with a single gene target on chromosome 4 in the upper panel and a histogram of the intensity data corresponding to 960 label-tags in the lower panel.

FIG. 24 shows a plot of the number of times each of the 960 label-tags was observed in ligations with low DNA target amounts.

FIG. 25 shows plots of label-tags observed in the mapped reads from the first sequencing run for chromosome 4 with the horizontal dashed line indicating the counting threshold applied and the vertical dashed line indicating the break separating the 192 negative controls from the expected label-tags (controls to the right of the line).

FIG. 26 shows a method for adding counting label-tags to polyadenylated RNA.

FIG. 27 shows another method for adding counting label-tags to polyadenylated RNA.

FIG. 28A shows a method for adding label-tags to targets using a primer that has a stem loop between two poly (dT) regions.

FIG. 28B shows amplification of the products of the method followed by fragmentation and adaptor ligation to generate a product to be sequenced.

DETAILED DESCRIPTION OF THE INVENTION

Reference will now be made in detail to exemplary embodiments of the invention. While the invention will be described in conjunction with the exemplary embodiments, it will be understood that they are not intended to limit the invention to these embodiments. On the contrary, the invention is intended to cover alternatives, modifications and equivalents, which may be included within the spirit and scope of the invention.

The invention has many preferred embodiments and relies on many patents, applications and other references for details known to those of the art. Therefore, when a patent, application, or other reference, such as a printed publication, is cited or repeated below, it should be understood that it is incorporated by reference in its entirety for all purposes and particularly for the proposition that is recited.

As used in this application, the singular form “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise. For example, the term “an agent” includes a plurality of agents, including mixtures thereof.

An individual is not limited to a human being, but may also be other organisms including, but not limited to, mammals, plants, bacteria, or cells derived from any of the above.

Throughout this disclosure, various aspects of this invention can be presented in a range format. It should be understood that the description in range format is merely for convenience and brevity and should not be construed as an inflexible limitation on the scope of the invention. Accordingly, the description of a range should be considered to have specifically disclosed all the possible subranges as well as individual numerical values within that range. For example, description of a range such as from 1 to 6 should be considered to have specifically disclosed subranges such as from 1 to 3, from 1 to 4, from 1 to 5, from 2 to 4, from 2 to 6, from 3 to 6 etc., as well as individual numbers within that range, for example, 1, 2, 3, 4, 5, and 6. This applies regardless of the breadth of the range.

Suitable samples for analysis may be derived from a variety of sources. Biological samples may be of any biological tissue or fluid or cells from any organism. Frequently the sample will be a “clinical sample” which is a sample derived from a patient. Clinical samples provide a rich source of information regarding the various states of gene expression and copy number. Typical clinical samples include, but are not limited to, sputum, blood, tissue or fine needle biopsy samples, urine, peritoneal fluid, and pleural fluid, or cells therefrom. Biological samples may also include sections of tissues, such as frozen sections or formalin-fixed sections taken for histological purposes, which may include formalin-fixed, paraffin embedded (FFPE) samples and samples derived therefrom. FFPE samples are a particularly important source for study of archived tissue as they can nucleic acids can be recovered from these samples even after long term storage of the samples at room temperature. See, for example, Specht et al. Am J. Path. (2001), 158(2):419-429. Nucleic acids isolated from fresh-frozen samples may also be analyzed using the disclosed methods.

The practice of the present invention may employ, unless otherwise indicated, conventional techniques and descriptions of organic chemistry, polymer technology, molecular biology (including recombinant techniques), cell biology, biochemistry, and immunology, which are within the skill of the art. Such conventional techniques include polymer array synthesis, hybridization, ligation, and detection of hybridization using a label. Specific illustrations of suitable techniques can be had by reference to the example herein below. However, other equivalent conventional procedures can, of course, also be used. Such conventional techniques and descriptions can be found in standard laboratory manuals such as Genome Analysis: A Laboratory Manual Series (Vols. I-IV), Using Antibodies: A Laboratory Manual, Cells: A Laboratory Manual, PCR Primer: A Laboratory Manual, and Molecular Cloning: A Laboratory Manual (all from Cold Spring Harbor Laboratory Press), Gait, “Oligonucleotide Synthesis: A Practical Approach” 1984, IRL Press, London, Nelson and Cox (2000), Lehninger et al., (2008) Principles of Biochemistry 5th Ed., W.H. Freeman Pub., New York, N.Y. and Berg et al. (2006) Biochemistry, 6^(th) Ed., W.H. Freeman Pub., New York, N.Y., all of which are herein incorporated in their entirety by reference for all purposes.

The present invention can employ solid substrates, including arrays in some preferred embodiments. Methods and techniques applicable to polymer (including protein) array synthesis have been described in U.S. Patent Pub. No. 20050074787, WO 00/58516, U.S. Pat. Nos. 5,143,854, 5,242,974, 5,252,743, 5,324,633, 5,384,261, 5,405,783, 5,424,186, 5,451,683, 5,482,867, 5,491,074, 5,527,681, 5,550,215, 5,571,639, 5,578,832, 5,593,839, 5,599,695, 5,624,711, 5,631,734, 5,795,716, 5,831,070, 5,837,832, 5,856,101, 5,858,659, 5,936,324, 5,968,740, 5,974,164, 5,981,185, 5,981,956, 6,025,601, 6,033,860, 6,040,193, 6,090,555, 6,136,269, 6,269,846 and 6,428,752, in PCT Publication No. WO 99/36760 and WO 01/58593, which are all incorporated herein by reference in their entirety for all purposes. Patents that describe synthesis techniques in specific embodiments include U.S. Pat. Nos. 5,412,087, 6,147,205, 6,262,216, 6,310,189, 5,889,165, and 5,959,098. Nucleic acid arrays are described in many of the above patents, but many of the same techniques may be applied to polypeptide arrays.

The present invention also contemplates many uses for polymers attached to solid substrates. These uses include gene expression monitoring, transcript profiling, library screening, genotyping, epigenetic analysis, methylation pattern analysis, tumor typing, pharmacogenomics, agrigenetics, pathogen profiling and detection and diagnostics. Gene expression monitoring and profiling methods have been shown in U.S. Pat. Nos. 5,800,992, 6,013,449, 6,020,135, 6,033,860, 6,040,138, 6,177,248 and 6,309,822. Genotyping and uses therefore are shown in U.S. Patent Publication Nos. 20030036069 and 20070065816 and U.S. Pat. Nos. 5,856,092, 6,300,063, 5,858,659, 6,284,460, 6,361,947, 6,368,799 and 6,333,179. Other uses are embodied in U.S. Pat. Nos. 5,871,928, 5,902,723, 6,045,996, 5,541,061, and 6,197,506.

The present invention also contemplates sample preparation methods in certain embodiments. Prior to or concurrent with analysis, the sample may be amplified by a variety of mechanisms. In some aspects nucleic acid amplification methods such as PCR may be combined with the disclosed methods and systems. See, for example, PCR Technology: Principles and Applications for DNA Amplification (Ed. H. A. Erlich, Freeman Press, NY, N.Y., 1992); PCR Protocols: A Guide to Methods and Applications (Eds. Innis, et al., Academic Press, San Diego, Calif., 1990); Mattila et al., Nucleic Acids Res. 19, 4967 (1991); Eckert et al., PCR Methods and Applications 1, 17 (1991); PCR (Eds. McPherson et al., IRL Press, Oxford); and U.S. Pat. Nos. 4,683,202, 4,683,195, 4,800,159, 4,965,188, and 5,333,675, each of which is incorporated herein by reference in their entireties for all purposes. Additional methods of sample preparation and techniques for reducing the complexity of a nucleic sample are described in Dong et al., Genome Research 11, 1418 (2001), in U.S. Pat. Nos. 6,300,070 (amplification on an array), 6,361,947, 6,391,592, 6,872,529 and 6,458,530 and U.S. Patent Pub. Nos. 20030096235, 20030082543, 20030039069, 20050079536, 20040072217, 20050142577, 20050233354, 20050227244, 20050208555, 20050074799, 20050042654, and 20040067493, which are each incorporated herein by reference in their entireties.

Many of the methods and systems disclosed herein utilize enzyme activities. Enzymes and related methods of use in molecular biology that may be used in combination with the disclosed methods and systems are reviewed, for example, in Rittie and Perbal, J. Cell Commun. Signal. (2008) 2:25-45, incorporated herein by reference in its entirety. A variety of enzymes are well known, have been characterized and many are commercially available from one or more supplier. Exemplary enzymes include DNA dependent DNA polymerases (such as those shown in Table 1 of Rittie and Perbal), RNA dependent DNA polymerase (see Table 2 of Rittie and Perbal), RNA polymerases (such as T7 and SP6), ligases (see Table 3 of Rittie and Perbal), enzymes for phosphate transfer and removal (see Table 4 of Rittie and Perbal), nucleases (see Table 5 of Rittie and Perbal), and methylases.

Other methods of genome analysis and complexity reduction include, for example, AFLP, see U.S. Pat. No. 6,045,994, which is incorporated herein by reference, and arbitrarily primed-PCR (AP-PCR) see McClelland and Welsh, in PCR Primer: A laboratory Manual, (1995) eds. C. Dieffenbach and G. Dveksler, Cold Spring Harbor Lab Press, for example, at p 203, which is incorporated herein by reference in its entirety.

Other suitable amplification methods include the ligase chain reaction (LCR) (for example, Wu and Wallace, Genomics 4, 560 (1989), Landegren et al., Science 241, 1077 (1988) and Barringer et al. Gene 89:117 (1990)), transcription amplification (Kwoh et al., Proc. Natl. Acad. Sci. USA 86, 1173 (1989) and WO88/10315), self-sustained sequence replication (Guatelli et al., Proc. Nat. Acad. Sci. USA, 87, 1874 (1990) and WO90/06995), selective amplification of target polynucleotide sequences (U.S. Pat. No. 6,410,276), consensus sequence primed polymerase chain reaction (CP-PCR) (U.S. Pat. No. 4,437,975), arbitrarily primed polymerase chain reaction (AP-PCR) (U.S. Pat. Nos. 5,413,909, 5,861,245), rolling circle amplification (RCA) (for example, Fire and Xu, PNAS 92:4641 (1995) and Liu et al., J. Am. Chem. Soc. 118:1587 (1996)) and U.S. Pat. No. 5,648,245, strand displacement amplification (see Lasken and Egholm, Trends Biotechnol. 2003 21(12):531-5; Barker et al. Genome Res. 2004 May; 14(5):901-7; Dean et al. Proc Natl Acad Sci USA. 2002; 99(8):5261-6; Walker et al. 1992, Nucleic Acids Res. 20(7):1691-6, 1992 and Paez, J. G., et al. Nucleic Acids Res. 2004; 32(9):e71), Qbeta Replicase, described in PCT Patent Application No. PCT/US87/00880 and nucleic acid based sequence amplification (NABSA). (See, U.S. Pat. Nos. 5,409,818, 5,554,517, and 6,063,603, each of which is incorporated herein by reference). Other amplification methods that may be used are described in, U.S. Pat. Nos. 6,582,938, 5,242,794, 5,494,810, 4,988,617, and US Pub. No. 20030143599 each of which is incorporated herein by reference. DNA may also be amplified by multiplex locus-specific PCR or using adaptor-ligation and single primer PCR (See Kinzler and Vogelstein, NAR (1989) 17:3645-53. Other available methods of amplification, such as balanced PCR (Makrigiorgos, et al. (2002), Nat Biotechnol, Vol. 20, pp. 936-9), may also be used.

Molecular inversion probes (“MIPs”) may also be used for amplification of selected targets. MIPs may be generated so that the ends of the pre-circle probe are complementary to regions that flank the region to be amplified. The gap can be closed by extension of the end of the probe so that the complement of the target is incorporated into the MIP prior to ligation of the ends to form a closed circle. The closed circle can be amplified and detected by sequencing or hybridization as previously disclosed in Hardenbol et al., Genome Res. 15:269-275 (2005) and in U.S. Pat. No. 6,858,412.

Methods of ligation will be known to those of skill in the art and are described, for example in Sambrook et at. (2001) and the New England BioLabs catalog both of which are incorporated herein by reference for all purposes. Methods include using T4 DNA Ligase which catalyzes the formation of a phosphodiester bond between juxtaposed 5′ phosphate and 3′ hydroxyl termini in duplex DNA or RNA with blunt and sticky ends; Taq DNA Ligase which catalyzes the formation of a phosphodiester bond between juxtaposed 5′ phosphate and 3′ hydroxyl termini of two adjacent oligonucleotides which are hybridized to a complementary target DNA; E. coli DNA ligase which catalyzes the formation of a phosphodiester bond between juxtaposed 5′-phosphate and 3′-hydroxyl termini in duplex DNA containing cohesive ends; and T4 RNA ligase which catalyzes ligation of a 5′ phosphoryl-terminated nucleic acid donor to a 3′ hydroxyl-terminated nucleic acid acceptor through the formation of a 3′→5′ phosphodiester bond, substrates include single-stranded RNA and DNA as well as dinucleoside pyrophosphates; or any other methods described in the art. Fragmented DNA may be treated with one or more enzymes, for example, an endonuclease, prior to ligation of adaptors to one or both ends to facilitate ligation by generating ends that are compatible with ligation.

Methods for ligating adaptors to fragments of nucleic acid are well known. Adaptors may be double-stranded, single-stranded or partially single-stranded. In preferred aspects adaptors are formed from two oligonucleotides that have a region of complementarity, for example, about 10 to 30, or about 15 to 40 bases of perfect complementarity, so that when the two oligonucleotides are hybridized together they form a double stranded region. Optionally, either or both of the oligonucleotides may have a region that is not complementary to the other oligonucleotide and forms a single stranded overhang at one or both ends of the adaptor. Single-stranded overhangs may preferably by about 1 to about 8 bases, and most preferably about 2 to about 4. The overhang may be complementary to the overhang created by cleavage with a restriction enzyme to facilitate “sticky-end” ligation. Adaptors may include other features, such as primer binding sites and restriction sites. In some aspects the restriction site may be for a Type IIS restriction enzyme or another enzyme that cuts outside of its recognition sequence, such as EcoP15I (see, Mucke et al. J Mol Biol 2001, 312(4):687-698 and U.S. Pat. No. 5,710,000 which is incorporated herein by reference in its entirety).

Methods for using mapping arrays see, for example, Applications of microarrays for SNP genotyping have been described in e.g., U.S. Pat. Nos. 6,300,063, 6,361,947, 6,368,799 and US Patent Publication Nos. 20040067493, 20030232353, 20030186279, 20050260628, 20070065816 and 20030186280, and Kennedy et al., Nat. Biotech. 21:1233-1237 (2003), Matsuzaki et al., Genome Res. 14:414-425 (2004), Matsuzaki et al., Nat. Meth. 1:109-111 (2004) and U.S. Patent Pub. Nos. 20040146890 and 20050042654, each incorporated herein by reference. Fixed content mapping arrays are available from Affymetrix, for example, the SNP 6.0 array and the AXIOM® array system. Selected panels of SNPs and markers (e.g. copy number markers) can also be interrogated using a panel of locus specific probes in combination with a universal array as described in Hardenbol et al., Genome Res. 15:269-275 (2005) and in U.S. Pat. No. 6,858,412. Universal tag arrays and reagent kits for performing such locus specific genotyping using panels of custom molecular inversion probes (MIPs) are available from Affymetrix.

Methods for analyzing chromosomal copy number using mapping arrays are disclosed, for example, in Bignell et al., Genome Res. 14:287-95 (2004), Lieberfarb, et al., Cancer Res. 63:4781-4785 (2003), Zhao et al., Cancer Res. 64:3060-71 (2004), Huang et al., Hum Genomics 1:287-299 (2004), Nannya et al., Cancer Res. 65:6071-6079 (2005), Slater et al., Am. J. Hum. Genet. 77:709-726 (2005) and Ishikawa et al., Biochem. and Biophys. Res. Comm., 333:1309-1314 (2005). Computer implemented methods for estimation of copy number based on hybridization intensity are disclosed in U.S. Patent Pub. Nos. 20040157243, 20050064476, 20050130217, 20060035258, 20060134674 and 20060194243.

Methods for conducting polynucleotide hybridization assays have been well developed in the art. Hybridization assay procedures and conditions will vary depending on the application and are selected in accordance with known general binding methods, including those referred to in: Maniatis et al. Molecular Cloning: A Laboratory Manual (2^(nd) Ed. Cold Spring Harbor, N.Y, 1989); Berger and Kimmel Methods in Enzymology, Vol. 152, Guide to Molecular Cloning Techniques (Academic Press, Inc., San Diego, Calif., 1987); Young and Davis, P.N.A.S, 80: 1194 (1983). Methods and apparatus for carrying out repeated and controlled hybridization reactions have been described in U.S. Pat. Nos. 5,871,928, 5,874,219, 6,045,996 and 6,386,749, 6,391,623 each of which are incorporated herein by reference.

The present invention also contemplates signal detection of hybridization between ligands in certain preferred embodiments. See U.S. Pat. Nos. 5,143,854, 5,578,832, 5,631,734, 5,834,758, 5,936,324, 5,981,956, 6,025,601, 6,141,096, 6,185,030, 6,201,639, 6,218,803, and 6,225,625 in U.S. Patent Pub. No. 20040012676 and in PCT Application PCT/US99/06097 (published as WO99/47964), each of which also is hereby incorporated by reference in its entirety for all purposes.

Methods and apparatus for signal detection and processing of intensity data are disclosed in, for example, U.S. Pat. Nos. 5,143,854, 5,547,839, 5,578,832, 5,631,734, 5,800,992, 5,834,758, 5,856,092, 5,902,723, 5,936,324, 5,981,956, 6,025,601, 6,090,555, 6,141,096, 6,185,030, 6,201,639; 6,218,803; and 6,225,625, in U.S. Patent Pub. Nos. 20040012676 and 20050059062 and in PCT Application PCT/US99/06097 (published as WO99/47964), each of which also is hereby incorporated by reference in its entirety for all purposes.

The practice of the present invention may also employ conventional biology methods, software and systems. Computer software products of the invention typically include computer readable medium having computer-executable instructions for performing the logic steps of the method of the invention. Suitable computer readable medium include floppy disk, CD-ROM/DVD/DVD-ROM, hard-disk drive, flash memory, ROM/RAM, magnetic tapes, etc. The computer-executable instructions may be written in a suitable computer language or combination of several languages. Basic computational biology methods are described in, for example, Setubal and Meidanis et al., Introduction to Computational Biology Methods (PWS Publishing Company, Boston, 1997); Salzberg, Searles, Kasif, (Ed.), Computational Methods in Molecular Biology, (Elsevier, Amsterdam, 1998); Rashidi and Buehler, Bioinformatics Basics: Application in Biological Science and Medicine (CRC Press, London, 2000) and Ouelette and Bzevanis Bioinformatics: A Practical Guide for Analysis of Gene and Proteins (Wiley & Sons, Inc., 2^(nd) ed., 2001). See also U.S. Pat. No. 6,420,108.

The present invention may also make use of various computer program products and software for a variety of purposes, such as probe design, management of data, analysis, and instrument operation. See, U.S. Pat. Nos. 5,593,839, 5,795,716, 5,733,729, 5,974,164, 6,066,454, 6,090,555, 6,185,561, 6,188,783, 6,223,127, 6,229,911 and 6,308,170. Computer methods related to genotyping using high density microarray analysis may also be used in the present methods, see, for example, US Patent Pub. Nos. 20050250151, 20050244883, 20050108197, 20050079536 and 20050042654. Additionally, the present disclosure may have preferred embodiments that include methods for providing genetic information over networks such as the Internet as shown in U.S. Patent Pub. Nos. 20030097222, 20020183936, 20030100995, 20030120432, 20040002818, 20040126840, and 20040049354.

An allele refers to one specific form of a genetic sequence (such as a gene) within a cell, an individual or within a population, the specific form differing from other forms of the same gene in the sequence of at least one, and frequently more than one, variant sites within the sequence of the gene. The sequences at these variant sites that differ between different alleles are termed “variances”, “polymorphisms”, or “mutations”. At each autosomal specific chromosomal location or “locus” an individual possesses two alleles, one inherited from one parent and one from the other parent, for example one from the mother and one from the father. An individual is “heterozygous” at a locus if it has two different alleles at that locus. An individual is “homozygous” at a locus if it has two identical alleles at that locus.

The term “polymorphism” as used herein refers to the occurrence of two or more genetically determined alternative sequences or alleles in a population. A polymorphic marker or site is the locus at which divergence occurs. Preferred markers have at least two alleles, each occurring at frequency of greater than 1%, and more preferably greater than 10% or 20% in a selected population. A polymorphism may comprise one or more base changes, an insertion, a repeat, or a deletion of one or more bases. Copy number variants (CNVs), transversions and other rearrangements are also forms of genetic variation. Polymorphic markers include restriction fragment length polymorphisms, variable number of tandem repeats (VNTR's), hypervariable regions, minisatellites, dinucleotide repeats, trinucleotide repeats, tetranucleotide repeats, simple sequence repeats, and insertion elements such as Alu. The allelic form occurring most frequently in a selected population is sometimes referred to as the wildtype form. Diploid organisms may be homozygous or heterozygous for allelic forms. A diallelic polymorphism has two forms. A triallelic polymorphism has three forms. Single nucleotide polymorphisms (SNPs) are a form of polymorphisms. SNPs are a common type of human genetic variation and are useful in the performance of genome wide association studies (GWAS). GWAS may be used, for example for the analysis of biological pathways, see Wang and Hakonarson, Nat. Rev. Genet. 2010, 11:843-854.

The term genotyping refers to the determination of the genetic information an individual carries at one or more positions in the genome. For example, genotyping may comprise the determination of which allele or alleles an individual carries for a single SNP or the determination of which allele or alleles an individual carries for a plurality of SNPs or CNVs. A diploid individual may be homozygous for each of the two possible alleles (for example, AA or BB) or heterozygous (for example, AB). For additional information regarding genotyping and genome structure see, Color Atlas of Genetics, Ed. Passarge, Thieme, New York, N.Y. (2001), which is incorporated by reference.

Normal cells that are heterozygous at one or more loci may give rise to tumor cells that are homozygous at those loci. This loss of heterozygosity (LOH) may result from structural deletion of normal genes or loss of the chromosome carrying the normal gene, mitotic recombination between normal and mutant genes, followed by formation of daughter cells homozygous for deleted or inactivated (mutant) genes; or loss of the chromosome with the normal gene and duplication of the chromosome with the deleted or inactivated (mutant) gene. LOH may be copy neutral or may result from a deletion or amplification.

The term “array” as used herein refers to an intentionally created collection of molecules which can be prepared either synthetically or biosynthetically. The molecules in the array can be identical or different from each other. The array can assume a variety of formats, for example, libraries of soluble molecules; libraries of compounds tethered to resin beads, silica chips, microparticles, nanoparticles or other solid supports.

The term “complementary” as used herein refers to the hybridization or base pairing between nucleotides or nucleic acids, such as, for instance, between the two strands of a double stranded DNA molecule or between an oligonucleotide primer and a primer binding site on a single stranded nucleic acid to be sequenced or amplified. See, M. Kanehisa Nucleic Acids Res. 12:203 (1984), incorporated herein by reference.

The term “copy number variation” or “CNV” refers to differences in the copy number of genetic information. In many aspects it refers to differences in the per genome copy number of a genomic region. For example, in a diploid organism the expected copy number for autosomal genomic regions is 2 copies per genome. Such genomic regions should be present at 2 copies per cell. For a recent review see Zhang et al. Annu. Rev. Genomics Hum. Genet. 2009. 10:451-81. CNV is a source of genetic diversity in humans and can be associated with complex disorders and disease, for example, by altering gene dosage, gene disruption, or gene fusion. They can also represent benign polymorphic variants. CNVs can be large, for example, larger than 1 Mb, but many are smaller, for example between 100 bp and 1 Mb. More than 38,000 CNVs greater than 100 bp (and less than 3 Mb) have been reported in humans. Along with SNPs these CNVs account for a significant amount of phenotypic variation between individuals. In addition to having deleterious impacts, e.g. causing disease, they may also result in advantageous variation.

Digital PCR is a technique where a limiting dilution of the sample is made across a large number of separate PCR reactions so that most of the reactions have no template molecules and give a negative amplification result. Those reactions that are positive at the reaction endpoint are counted as individual template molecules present in the original sample in a 1 to 1 relationship. See Kalina et al. NAR 25:1999-2004 (1997) and Vogelstein and Kinzler, PNAS 96:9236-9241 (1999). This method is an absolute counting method where solutions are partitioned into containers until there is an average probability of one molecule per two containers or when, P₀=(1−e^(−n/c))=½; where n is the number of molecules and c is the number of containers, or n/c is 0.693. Quantitative partitioning is assumed, and the dynamic range is governed by the number of containers available for stochastic separation. The molecules are then detected by PCR and the number of positive containers is counted. Each successful amplification is counted as one molecule, independent of the actual amount of product. PCR-based techniques have the additional advantage of only counting molecules that can be amplified, e.g. that are relevant to the massively parallel PCR step in the sequencing workflow. Because digital PCR has single molecule sensitivity, only a few hundred library molecules are required for accurate quantification. Elimination of the quantification bottleneck reduces the sample input requirement from micrograms to nanograms or less, opening the way for minute and/or precious samples onto the next-generation sequencing platforms without the distorting effects of pre-amplification. Digital PCR has been used to quantify sequencing libraries to eliminate uncertainty associated with the construction and application of standard curves to PCR-based quantification and enable direct sequencing without titration runs. See White et al. BMC Genomics 10: 116 (2009). To vary dynamic range, micro-fabrication can be used to substantially increase the number of containers. See, Fan et al. Am J Obstet Gynecol 200, 543 e1 (May, 2009).

Similarly, in stochastic labeling as disclosed herein, the same statistical conditions are met when P₀=(1−e^(−n/m))=½; where m is the number of label-tags, and one half of the label-tags will be used at least once when n/m=0.693. The dynamic range is governed by the number of label-tags used, and the number of label-tags can be easily increased to extend the dynamic range. The number of containers in digital PCR plays the same role as the number of label-tags in stochastic labeling and by substituting containers for label-tags identical statistical equations may be applied. Using the principles of physical separation, digital PCR stochastically expands identical molecules into physical space, whereas the principle governing stochastic labeling is identity based and expands identical molecules into identity space.

The term “hybridization” as used herein refers to the process in which two single-stranded polynucleotides bind non-covalently to form a stable double-stranded polynucleotide; triple-stranded hybridization is also theoretically possible. The resulting (usually) double-stranded polynucleotide is a “hybrid.” The proportion of the population of polynucleotides that forms stable hybrids is referred to herein as the “degree of hybridization.” Hybridizations may be performed under stringent conditions, for example, at a salt concentration of no more than 1 M and a temperature of at least 25° C. For example, conditions of 5×SSPE (750 mM NaCl, 50 mM NaPhosphate, 5 mM EDTA, pH 7.4) and a temperature of 25-30° C. are suitable for allele-specific probe hybridizations. For stringent conditions, see, for example, Sambrook, Fritsche and Maniatis. “Molecular Cloning A laboratory Manual” 2^(nd) Ed. Cold Spring Harbor Press (1989) which is hereby incorporated by reference in its entirety for all purposes above. In some aspects salt concentrations for hybridization are preferably between about 200 mM and about 1M or between about 200 mM and about 500 mM. Hybridization temperatures can be as low as 5° C., but are typically greater than 22° C., more typically greater than about 30° C., and preferably in excess of about 37° C. Longer fragments may require higher hybridization temperatures for specific hybridization. As other factors may affect the stringency of hybridization, including base composition and length of the complementary strands, presence of organic solvents and extent of base mismatching, the combination of parameters is more important than the absolute measure of any one alone.

The term “mRNA” or sometimes refer by “mRNA transcripts” as used herein, include, but not limited to pre-mRNA transcript(s), transcript processing intermediates, mature mRNA(s) ready for translation and transcripts of the gene or genes, or nucleic acids derived from the mRNA transcript(s). Transcript processing may include splicing, editing and degradation. As used herein, a nucleic acid derived from an mRNA transcript refers to a nucleic acid for whose synthesis the mRNA transcript or a subsequence thereof has ultimately served as a template. Thus, a cDNA reverse transcribed from an mRNA, an RNA transcribed from that cDNA, a DNA amplified from the cDNA, an RNA transcribed from the amplified DNA, etc., are all derived from the mRNA transcript and detection of such derived products is indicative of the presence and/or abundance of the original transcript in a sample. Thus, mRNA derived samples include, but are not limited to, mRNA transcripts of the gene or genes, cDNA reverse transcribed from the mRNA, cRNA transcribed from the cDNA, DNA amplified from the genes, RNA transcribed from amplified DNA, and the like.

Other classes or RNAs are also expressed, including, for example, ribosomal RNA, snRNA, miRNA and siRNA. Recent evidence suggests that the human transcriptome contains many functional RNA transcripts which are not translated into proteins. These non-coding RNAs have been recognized as important to a more complete understanding of biology. Mature miRNAs are relatively small (21-23 nucleotides) RNA duplexes that act as translational repressors of protein expression. The guide strand of a miRNA interacts with proteins to form RNA-Induced Silencing Complexes (RISC) in the cell. These sequence-specific ribonucleoprotein complexes bind target mRNAs typically in the 3′UTR and can subsequently silence gene expression either through directed mRNA degradation or by simply sequestering the target mRNA in an ineffectual form (Lee et al., Cell (1993), 75: 843-854; Bartel, Cell (2009), 136: 215-233). It has been demonstrated that miRNA based regulation plays a significant role in routine cellular processes including metabolism (Esau et al, Cell Met. 2006, v. 3, p 87-98), development (Carthew et al., Cell 2009, v. 137, p. 273-282), and even apoptosis (Cheng et al, Nucl. Acids Res. 2005, v. 33, p 1290-1297). Further research has revealed that miRNAs play critical roles in diverse disease processes such as hepatitis C (Jopling et al., Science 2005, v. 309, p. 1577-1581), diabetes (Poy et al., Nature 2004, v. 432, p. 226-230), and most notably multiple cancer types (Hammond, Can. Chemo. Pharma. 2006 v. 58, s63-s68; Calin et al., Cancer Res. 2006, v. 66, p. 7390-7394) including leukemia (Calin et al., PNAS 2002, v. 101, p. 2999-3004) and glioma (Corsten et al., Cancer Res. 2007, v. 67, p. 8994-9000). Over one thousand miRNAs have now been identified in animals, but only a few individual miRNAs have been linked to specific functions. Methods of the invention disclosed herein can be used for inactivation of relatively short regulatory non-coding RNAs, such as micro RNAs (miRNAs), Piwi-interacting RNAs (piRNAs), snoRNAs, snRNAs, moRNAs, PARs, sdRNAs, tel-sRNAs, crasiRNAs, and small interfering RNAs (siRNAs). Methods of the invention can also be used for long non-coding RNAs (long ncRNAs), traditional non-coding tRNAs and ribosomal RNA (rRNA).

The term “nucleic acid” as used herein refers to a polymeric form of nucleotides of any length, either ribonucleotides, deoxyribonucleotides or peptide nucleic acids (PNAs), that comprise purine and pyrimidine bases, or other natural, chemically or biochemically modified, non-natural, or derivatized nucleotide bases. The backbone of the polynucleotide can comprise sugars and phosphate groups, as may typically be found in RNA or DNA, or modified or substituted sugar or phosphate groups. A polynucleotide may comprise modified nucleotides, such as methylated nucleotides and nucleotide analogs. The sequence of nucleotides may be interrupted by non-nucleotide components. Thus the terms nucleoside, nucleotide, deoxynucleoside and deoxynucleotide generally include analogs such as those described herein. These analogs are those molecules having some structural features in common with a naturally occurring nucleoside or nucleotide such that when incorporated into a nucleic acid or oligonucleoside sequence, they allow hybridization with a naturally occurring nucleic acid sequence in solution. Typically, these analogs are derived from naturally occurring nucleosides and nucleotides by replacing and/or modifying the base, the ribose or the phosphodiester moiety. The changes can be tailor made to stabilize or destabilize hybrid formation or enhance the specificity of hybridization with a complementary nucleic acid sequence as desired.

The term “oligonucleotide” or sometimes refer by “polynucleotide” as used herein refers to a nucleic acid ranging from at least 2, preferable at least 8, and more preferably at least 20 nucleotides in length or a compound that specifically hybridizes to a polynucleotide. Polynucleotides of the present invention include sequences of deoxyribonucleic acid (DNA) or ribonucleic acid (RNA) which may be isolated from natural sources, recombinantly produced or artificially synthesized and mimetics thereof. A further example of a polynucleotide of the present invention may include non natural analogs that may increase specificity of hybridization, for example, peptide nucleic acid (PNA) linkages and Locked Nucleic Acid (LNA) linkages. The LNA linkages are conformationally restricted nucleotide analogs that bind to complementary target with a higher melting temperature and greater mismatch discrimination. Other modifications that may be included in probes include: 2′OMe, 2′OAllyl, 2′O-propargyl, 2′O-alkyl, 2′ fluoro, 2′ arabino, 2′ xylo, 2′ fluoro arabino, phosphorothioate, phosphorodithioate, phosphoroamidates, 2′Amino, 5-alkyl-substituted pyrimidine, 5-halo-substituted pyrimidine, alkyl-substituted purine, halo-substituted purine, bicyclic nucleotides, 2′MOE, LNA-like molecules and derivatives thereof. The invention also encompasses situations in which there is a nontraditional base pairing such as Hoogsteen base pairing which has been identified in certain tRNA molecules and postulated to exist in a triple helix. “Polynucleotide” and “oligonucleotide” are used interchangeably in this application.

The term “primer” as used herein refers to a single-stranded oligonucleotide capable of acting as a point of initiation for template-directed DNA synthesis under suitable conditions for example, buffer and temperature, in the presence of four different nucleoside triphosphates and an agent for polymerization, such as, for example, DNA or RNA polymerase or reverse transcriptase. The length of the primer, in any given case, depends on, for example, the intended use of the primer, and generally ranges from 15 to 30 nucleotides. Short primer molecules generally require cooler temperatures to form sufficiently stable hybrid complexes with the template. A primer need not reflect the exact sequence of the template but must be sufficiently complementary to hybridize with such template. The primer site is the area of the template to which a primer hybridizes. The primer pair is a set of primers including a 5′ upstream primer that hybridizes with the 5′ end of the sequence to be amplified and a 3′ downstream primer that hybridizes with the complement of the 3′ end of the sequence to be amplified.

The term “probe” as used herein refers to a surface-immobilized molecule that can be recognized by a particular target. See U.S. Pat. No. 6,582,908 for an example of arrays having all possible combinations of probes with 10, 12, and more bases. Examples of probes that can be investigated by this invention include, but are not restricted to, agonists and antagonists for cell membrane receptors, toxins and venoms, viral epitopes, hormones (for example, opioid peptides, steroids, etc.), hormone receptors, peptides, enzymes, enzyme substrates, cofactors, drugs, lectins, sugars, oligonucleotides, nucleic acids, oligosaccharides, proteins, and monoclonal antibodies.

The term “solid support”, “support”, and “substrate” as used herein are used interchangeably and refer to a material or group of materials having a rigid or semi-rigid surface or surfaces. In many embodiments, at least one surface of the solid support will be substantially flat, although in some embodiments it may be desirable to physically separate synthesis regions for different compounds with, for example, wells, raised regions, pins, etched trenches, or the like. According to other embodiments, the solid support(s) will take the form of beads, resins, gels, microspheres, or other geometric configurations. See U.S. Pat. No. 5,744,305 and US Patent Pub. Nos. 20090149340 and 20080038559 for exemplary substrates.

The terms “label-tag”, “identifier” and “counter” as used herein refer to the information that is added to individual occurrences of species of molecules to be counted using the methods disclosed herein. Libraries of label-tags having a diversity of unique label-tags, for example about 1,000, about 5,000, about 10,000, about 100,000 or more than 100,000 may be used to uniquely identify occurrences of target species thereby marking each species with an identifier that can be used to distinguish between two otherwise identical or nearly identical targets. For example, each label-tag may be a short string of nucleotides that can be attached to different copies of an mRNA, for example, a first label-tag may be 5′GCATCTTC3′ and a second may be 5′CAAGTAAC3′. Each has a unique identity that can be determined by determining the identity and order of the bases in the label-tag. Although nucleic acids are used throughout as a preferred embodiment of label-tag, one of skill in the art will appreciate that a number of types of molecules or items that can be generated with the diversity needed may be used as label-tags. Label-tags should be compounds, structures or elements that are amenable to at least one method of detection that allows for discrimination between different label-tags and should be associable in some means with the elements to be counted. For example, a pool of label-tags may be comprises of a collection of different semiconductor nanocrystals, metal compounds, peptides, antibodies, small molecules, isotopes, particles or structures having different shapes, colors, barcodes or diffraction patterns associated therewith or embedded therein, strings of numbers, random fragments of proteins or nucleic acids, or different isotopes (see, Abdelrahman, A. I. et al. Journal of Analytical Atomic Spectrometry 25 (3):260-268, 2010 for use of metal containing polystyrene beads as standards for mass cytometry, incorporated herein by reference). Pools of label-tags may be partitioned into distinct sets that can be attached to separate sample mixtures and then combined for later analysis. For example, a set of 1,000,000 different label-tags could be physically divided into 10 sets of 100,000 different label-tags and each could be used to label-tag a different mixture. The identity of the label-tags in each set can be used as an indication of the original source. Counting of multiple samples in parallel can be facilitated.

The term “detectable label” as used herein refers to any chemical moiety attached to a nucleotide, nucleotide polymer, or nucleic acid binding factor, wherein the attachment may be covalent or non-covalent. Preferably, the label is detectable and renders the nucleotide or nucleotide polymer detectable to the practitioner of the invention. Detectable labels that may be used in combination with the methods disclosed herein include, for example, a fluorescent label, a chemiluminescent label, a quencher, a radioactive label, biotin and gold, or combinations thereof. Detectable labels include luminescent molecules, fluorochromes, fluorescent quenching agents, colored molecules, radioisotopes or scintillants. Detectable labels also include any useful linker molecule (such as biotin, avidin, streptavidin, HRP, protein A, protein G, antibodies or fragments thereof, Grb2, polyhistidine, Ni²+, FLAG tags, myc tags), heavy metals, enzymes (examples include alkaline phosphatase, peroxidase and luciferase), electron donors/acceptors, acridinium esters, dyes and calorimetric substrates. It is also envisioned that a change in mass may be considered a detectable label, as is the case of surface plasmon resonance detection. The skilled artisan would readily recognize useful detectable labels that are not mentioned above, which may be employed in the operation of the present invention.

A stochastic process is the counterpart to a deterministic process. Instead of dealing with only one possible “reality” of how the process might evolve under time, in a stochastic or random process there is some indeterminacy in its future evolution described by probability distributions. This means that even if the initial condition (or starting point) is known, there are many possibilities the process might go to, but some paths are more probable and others less. When all of the molecules in a uniform mixture of fixed volume collide and react randomly, the chemical events follow a stochastic process governed in part by the molecule concentration of each species (D. T. Gillespie, The Journal of Physical Chemistry 81, 2340 (1977)).

In the simplest possible case, a stochastic process amounts to a sequence of random variables known as a time series. Another basic type of a stochastic process is a random field, whose domain is a region of space, in other words, a random function whose arguments are drawn from a range of continuously changing values. One approach to stochastic processes treats them as functions of one or several deterministic arguments (“inputs” or “time”) whose values (“outputs”) are random variables: non-deterministic (single) quantities which have certain probability distributions. Random variables corresponding to various times (or points, in the case of random fields) may be completely different. The main requirement is that these different random quantities all have the same “type”. Although the random values of a stochastic process at different times may be independent random variables, they often exhibit complicated statistical correlations. Familiar examples of processes modeled as stochastic time series include stock market and exchange rate fluctuations, signals such as speech, audio and video, medical data such as a patient's EKG, EEG, blood pressure or temperature, and random movement such as Brownian motion or random walks.

Stochastic Labeling of Individual Molecules

Methods are disclosed herein that may be applied to determining small numbers of biological molecules and their changes in response to, for example, cellular response, differentiation or signal transduction. The methods may also be used in performing a wide variety of clinical measurements. Although many analytical methods have been developed to measure the relative abundance of different molecules through sampling (e.g., microarrays and sequencing), the methods disclosed herein are able to determine the absolute number of molecules in a sample.

The stochastic labeling methods may also be generalized as follows. Consider a given target sequence defined as T={t₁, t₂ . . . t_(n)}; where n is the number of copies of T. A set of label-tags is defined as L={l₁, l₂ . . . l_(m)}; where m is the number of different label-tags. T reacts stochastically with L, such that each t becomes attached to one l. If the l's are in non-depleting excess, each t will choose one/randomly, and will take on a new identity l_(i)t_(j); where l_(i) is chosen from L and j is the j^(th) copy from the set of n molecules. We identify each new molecule l_(i)t_(j) by its label-tag subscript and drop the subscript for the copies of T, because they are identical. The new collection of molecules becomes T*=l₁t+l₂t+ . . . l_(i)t; where l_(i) is the i^(th) choice from the set of m label-tags. It is important to emphasize that the subscripts of l at this point refer only to the i^(th) choice and provide no information about the identity of each l. In fact, l₁ and l₂ will have some probability of being identical, depending upon the diversity m of the set of label-tags. Overall, T* will contain a set of k unique label-tags resulting from n targets choosing from the non-depleting reservoir of m label-tags. Or, T*(m,n)={tl_(k)}; where k represents the number of unique label-tags that have been captured. In all cases, k will be smaller than m, approaching m only when n becomes very large. We can define the stochastic attachment of the set of label-tags on a target using a stochastic operator S with m members, acting upon a target population of n, such that S(m)T(n)=T*(m,n) generating the set {l_(k)t}.

Furthermore, because S operates on all molecules independently, it can act on many different target sequences. Hence, the method can simultaneously count copies of multiple target sequences by combining the information of target sequence and label. The probability of the number of label-tags generated by the number of trials n, from a diversity of m, can be approximated by the Poisson equation, P_(x)=[(n/m)^(x)/x!]e^(−(n/m)). Then P₀ is the probability that a label-tag will not be chosen in n trials, and therefore, 1−P₀ is the probability that a label-tag will occur at least once. It follows that the number of unique label-tags captured is given by: k=m(1−P₀)=m[1−e^(−(n/m))]. Given k, we can calculate n. In addition to using the Poisson approximation, the relationship for k, n and m can be described analytically using the binomial distribution, or simulated using a random number generator, each yielding similar results.

The stochastic labeling process employed herein can be generalized as follows for illustrative purposes. Consider n copies of a given target molecule T, where T={t_(j), j=1, 2, . . . , n}, and a non-depleting reservoir of m diverse label-tags L, where L={l_(i), i=1, 2, . . . , m}. T reacts with L stochastically, such that each t_(j) will choose exactly one l_(i(j)), 1≦i(j)≦m to take on a new identity l_(i(j))t_(j), and may be identified by its label-tag subscript (the subscript j for the copy of target molecule t_(j) may be dropped). Therefore, the new collection of molecules T* may be denoted as T*={l _(i(j)) t,j=1,2, . . . ,n,1≦i(j)≦m}.

When different copies of the target molecules react with the same label-tag, i(j) for those molecules will assume the same value, therefore, the number of uniquely labeled target molecules k cannot be greater than m. The stochastic reaction of the set of label-tags on a target may be described by a stochastic operator S with m members, acting upon a target population of n, such that S(m)T(n)=ST=T*(m,n) generating the set T*={l_(i(j))t, j=1, 2, . . . , n, 1≦i(j)≦m}. For simplicity, we may write T*={l_(k)t}. Furthermore, since S operates on all molecules independently, it will act on many different target sequences and the method can be expanded to count copies of multiple target sequences, w,

simultaneously: ST^(w)=ST₁+ST₂+ . . . +ST_(w)=T₁*+T₂*+ . . . T_(w)*={l_(k)t}₁+{l_(k)t}₂+ . . . +{l_(k)t}_(w), where each T_(l)*, i=1, 2, . . . , w consists of a set {l_(k)t}_(l). The net result of S operating on a specific target population is to map the number of molecules, n, of that target, to the number of distinct label-tags captured, k, which is a random variable.

Because target molecules randomly react with a label-tag with probability

$\frac{1}{m},$ the probability of a label-tag being captured by exactly x out of n copies of a target molecule can be modeled as a Binomial distribution,

${{P(x)} = {\frac{n!}{{x!}{\left( {n - x} \right)!}}\left( \frac{1}{m} \right)^{x}\left( {1 - \frac{1}{m}} \right)^{n - x}}},$ where x! denotes the factorial of x. The probability that a label-tag will not be captured by any copy of the target molecule is P(0)=(1−1/m)^(n), and the probability that a label-tag will be captured at least once is 1−P(0). When n→∞ and 1/m→0 in the way that n/m→λ, P(x) converges to the Poisson distribution with mean λ, i.e.,

${P(x)} = {\frac{\lambda^{x}}{x!}{{\mathbb{e}}^{- \lambda}.}}$

To compute the number of unique label-tags captured by n copies of a target molecule, an index random variable, x may be introduced, which is 1 if a label-tag has been captured at least once, and 0 otherwise. The number of unique label-tags captured is thus

$k = {\sum\limits_{i = 1}^{m}{X_{i}.}}$ The mean and variance of k can be derived,

$\begin{matrix} {\mspace{79mu}{{E\lbrack k\rbrack} = {m\left\lbrack {1 - \left( {1 - \frac{1}{m}} \right)^{n}} \right\rbrack}}} & (1) \\ {{{Var}\lbrack k\rbrack} = {{{m\left\lbrack {1 - \left( {1 - \frac{1}{m}} \right)^{n}} \right\rbrack}\left( {1 - \frac{1}{m}} \right)^{n}} + {{m\left( {m - 1} \right)}\left\lbrack {\left( {1 - \frac{2}{m}} \right)^{n} - \left( {1 - \frac{1}{m}} \right)^{2\; n}} \right\rbrack}}} & (2) \end{matrix}$

Similarly, to compute the number of label-tags captured by exactly x copies of a target molecule, we introduce another index random variable, Y_(l), which is 1 if a label-tag has been captured exactly x times, and 0 otherwise. The number of label-tags captured x times is thus

$t = {\sum\limits_{i = 1}^{m}{Y_{i}.}}$ The mean and variance of t are,

$\begin{matrix} {\mspace{79mu}{{E\lbrack t\rbrack} = {\frac{m \cdot {n!}}{{x!}{\left( {n - x} \right)!}}\left( \frac{1}{m} \right)^{x}\left( {1 - \frac{1}{m}} \right)^{n - x}}}} & (3) \\ {{{Var}\lbrack t\rbrack} = {{A\left( {1 - A} \right)} + {\left( {m - 1} \right){m \cdot \begin{pmatrix} n \\ {2\; x} \end{pmatrix} \cdot \left( \frac{2}{m} \right)^{2\; x}}\left( {1 - \frac{2}{m}} \right)^{n - {2\; x}}\begin{pmatrix} {2\; x} \\ x \end{pmatrix}\left( \frac{1}{2} \right)^{2\; x}}}} & (4) \end{matrix}$

where

${A = {{m \cdot \begin{pmatrix} n \\ x \end{pmatrix}}\left( \frac{1}{m} \right)^{x}\left( {1 - \frac{1}{m}} \right)^{n - x}}},$ and the combination

$\begin{pmatrix} n \\ x \end{pmatrix} = {\frac{n!}{{x!}{\left( {n - x} \right)!}}.}$ The equations were experimentally validated by performing numerical simulations with 5000 independent runs for each simulated case. Complete agreement with the analytical solutions was observed.

The theoretical outcome of stochastic labeling is illustrated by examining the graph of k verses n (curve 1101 in FIG. 11) calculated using a label-tag diversity (m) of 960 and assuming a non-depleting reservoir. As expected, the number of unique label-tags captured depends on the ratio of molecules to label-tags, n/m. When n is much smaller than m, each molecule almost always captures a unique label-tag, and counting k is equivalent to counting n. As n increases, k increases more slowly as given by equation 1, and yet remains a very precise estimate of n. For example, when n/m is ˜0.01, the ratio of unique label-tags to molecules k/n˜0.99, and we expect an increase of 10 molecules will generate 10+/−X new label-tags. As n/m approaches 0.5 (i.e., ˜480 molecules reacted with 960 label-tags), k/n˜0.79 and ˜6+/−X new label-tags are expected with an increase of 10 molecules. At high n/m, k increases more slowly as label-tags in the library are more likely to be captured more than once. Curve 1101 shows the number of label-tags captured at least once, curve 1102 is the number of label-tags chosen exactly once, and curve 1103 shows the number of label-tags chosen exactly twice as n increases. Curve 1101 shows the number of label-tags captured at least once. Equation (1) above was used to calculate the at least once curve, equation (2) the exactly once curve and equation (3) the exactly twice curve. The error bars indicate one standard deviation from the corresponding mean value.

A more complete description of the number of times a label-tag is chosen as a function of n is shown in FIGS. 15 and 16 (which correspond to FIGS. S1 and S2 in Fu et al. PNAS, 108(22):9026-9031 (2011), which is incorporated herein in its entirety by reference). FIG. 15, plots the expected label-tag usage (y axis) when ligating to a given number of target molecules (x axis). Each copy of a target molecule randomly ligates to only a single copy of one of 1000 distinct label-tags equally represented in a library pool in non-depleting quantities. The number of occurrences that each label-tag is used is plotted as indicated. The expected label-tag usage was obtained from Eqs. (1) and (3). Ratios can also be expressed as m to n (or m/n) which may be, for example, greater than 50, 100, 500 or 1,000. FIG. 16 shows the predicted target molecule counting efficiency (Y-axis) based on libraries of 1000, 2000, 4000, 8000 or 10,000 label-tags (X-axis). Counting efficiency is expressed as the ratio of label-tags observed at least once over the number of target molecules present. At lower target numbers (inset plot) a near-linear relationship is expected, but counting efficiency decreases nonlinearly upon increased repetitive usage of the same label-tags. Larger numbers of label-tags have higher counting efficiencies.

Methods for performing single molecule digital counting by the stochastic labeling of a collection of identical molecules are disclosed. As illustrated in FIGS. 1, 2A and 2B, each copy of a molecule (from a collection of identical target molecules (target types 203 a, 203 b and 203 c, in a mixture 203) randomly captures a label-tag by choosing from a large, non-depleting reservoir of diverse label-tags 201. The uniqueness of each labeled molecule is governed by the statistics of random choice, and depends on the number of copies of identical molecules in the collection compared to the diversity of label-tags. Once the molecules are labeled each has been given a unique identity and can now be separately detected. In some aspects, it is preferable to first amplify the labeled targets prior to detection so that simple present/absent threshold detection methods can be used. Counting the number of label-tags is used to determine the original number of molecules in solution. In further aspects, the molecules to be counted are each members of a class that shares some common feature, for example, they may each be a single copy of a particular gene sequence or nucleic acid sequence. Counting may be applied, for example, to mRNA targets, including splicing products and alternatively spliced products and pre-mRNA. The methods may be used for counting of short regulatory non-coding RNAs, such as micro RNAs (miRNAs), Piwi-interacting RNAs (piRNAs), snoRNAs, snRNAs, moRNAs, PARs, sdRNAs, tel-sRNAs, crasiRNAs, and small interfering RNAs (siRNAs). Methods of the invention can also be used for long non-coding RNAs (long ncRNAs), traditional non-coding tRNAs, and ribosomal RNA (rRNA).

Similarly, counting may be applied to DNA, for example, gene copy number, chromosome number, mitochondrial DNA, bacterial genomes, pathogen nucleic acid, viral nucleic acids and the like. Counting may be applied in research of disease in humans or other mammals or agricultural organisms, e.g. cattle, chicken, wheat, rice, fish, etc. Counting may also be applied to counting aspects of microbes, such as environmental measurements, e.g. water quality testing. The methods may be particularly useful where small numbers of items are to be counted and an accurate count is desirable rather than a relative estimate.

FIG. 1 illustrates the labeling process schematically. The different label-tags or identifiers (represented by different shapes) from the pool of label-tags 201, {l₁, l₂ . . . l_(m)} are attached to each of 4 different copies of the same target “t”. Label-tag 20, l₂₀ is attached to t₁, label-tag 107 (l₁₀₇) to t₂, label-tag 477 (l₄₇₇) to t₃ and label-tag 9 (l₉) to t₄. The target-label-tag products, t₁l₂₀, t₂l₁₀₇, t₃l₄₇₇ and t₄l₉, are then amplified to generate four unique populations in a pool of amplified targets 205, each population representing a single occurrence of the target in the starting sample. Each target molecule randomly captures and joins with a label-tag by choosing from a large, nondepleting reservoir of m label-tags. Each resulting labeled target molecule takes on a new identity. The subsequent diversity of the labeled molecules is governed by the statistics of random choice, and depends on the number of copies of identical molecules in the collection compared to the number of kinds of label-tags. Once the molecules are labeled, they can be amplified so that simple present/absent threshold detection methods can be used for each. Counting the number of distinctly labeled targets reveals the original number of molecules of each species.

FIG. 2A illustrates a method for comparing two samples, identified as sample 1 and 2. The target 203 Gene A is present in 2 copies in sample 1 and 8 copies in sample 2. Both samples have non-target molecules 204. The label-tags 201 are combined with the samples and target molecules are attached to individual label-tag molecules in a stochastic manner. The targets with attached label-tags are hybridized to an array 211 having many features (illustrated schematically as squares), there is a feature for each possible target-label-tag combination. Some of the features are labeled, for example, 209 and others are not, for example, 207. The labeled features indicate the presence of a specific target-label-tag combination and each corresponds to a count. As shown for gene A in sample 1 there are two labeled features so the count is 2. For Gene A in sample 2 there are 8 labeled features so the count is 8.

FIG. 2C shows a further schematic illustration of one embodiment. A library of different label-tag sequences 201 (here shown as identical lines) is combined with a sample that includes an unknown number of each of several targets of interest in a mixture of targets 203. Three different species of target are shown, 203 a, 203 b and 203 c, present at 4, 6 and 3 copies respectively (non-targets may be present but are not shown). The individual label-tag oligonucleotides from library 201 are covalently attached to the different targets to form target-label-tag molecules 205. Each target has a collection of different label-tag molecules 205 a, 205 b and 205 c (again present at 4, 6 and 3 copies respectively) and within each target-specific collection the members differ in the label-tag oligo that is attached, so that each different target occurrence is uniquely marked with a different label-tag from the pool 201. On the array 207, each target is tiled in combination with all possible label-tag combinations represented with each different combination being present at a different known or determinable location on the array. In the figure each different possible combination of target and label-tag is represented by a single probe for illustration purposes, but on the array each different probe is preferably present in a feature having multiple copies of the same probe sequence. The array is divided into subarrays 207 a, 207 b and 207 c for illustrative purposes, each corresponding to a different target species (203 a, 203 b or 203 c respectively). The upper portion 209 of the probes (shown as vertical lines) varies at each feature according to the different label-tag. The lower portion 213 is the same for all features of each subarray and is complementary to the target. Preferably there is a different probe for each possible combination of label-tag and target. For example, if there are three targets being interrogated and 1000 different label-tags there would be 3,000 different probe features (3×1000). After hybridization individual features of the array are labeled through hybridization of the complementary target-label-tag molecule to the feature. The figure shows a detectable label 211, for example a biotin labeled nucleotide, may be used to detect features where a target-label-tag is hybridized.

Although the array illustrated in FIG. 2C is shown as a single planar support, any type of array could be used. In many aspects the methods do not require that the identity of the probe at a given feature be known or determinable and this allows for many different types of arrays to be used. Because the readout can be simply binary (i.e. yes, the feature is labeled or no, the feature is not labeled) it is not necessary to determine which probe sequence is present at a given feature. If a single target is being analyzed such that all features of the array correspond to the same target, the number of labeled features corresponds to the count and it is not necessary to determine which label-tags are being counted. The array can be one or more solid supports with different probes arranged in features at known or determinable locations or the probes may be arranged in a random manner where the region of the probe that is complementary to the label-tags is not known. This allows for a variety of synthesis approaches in addition to methods where the sequence to be synthesized or deposited at any given feature is known, for example, synthesis may include a pooled synthesis approach.

The array may also be beads or microparticles in solution. Different beads may be labeled with different probes and detection may be by arranging the beads on a solid support and imaging the beads on the support, (see for example, Oliphant et. al., Biotechniques 2002, 56-8, 60-1 and Kuhn et al. Genome Res. 2004 14(11):2347-56) or the beads may be imaged in solution as they flow through a detection chamber, see for example, Dunbar, S A, Clin Chim Acta. (2006), 363(1-2):71-82. A differentially identifiable bead type can be used for each target and within that bead type different individual beads can be attached to different target-label-tag probes. Each bead that is labeled can be counted as an occurrence of that target. Methods for making and using microparticles are also disclosed in U.S. Pat. Nos. 7,745,091 and 7,745,092 and PCT Publication No. WO 2007/081410, each of which is incorporated herein by reference in their entireties. Probes may be attached to a microparticle carrying a distinguishable code that may be characteristic of a target being counted. Such microparticles are preferably encoded such that the identity or type of a probe borne by a microparticle can be determined from a distinguishable code. The code can be in the form of a tag, which may itself be a probe, such as an oligonucleotide, a detectable label, such as a fluorophore, or embedded in the microparticle, for example, as a bar code. Microparticles bearing different probes may have different codes or the code may indicate members of a class of probes, for example, all probes for a given target, the probes varying in the label-tag region. Microparticles are typically distributed on a support by a sorting process in which a collection of microparticles are placed on the support and the microparticles distributed on the support. The location of the microparticles after distribution on the support can be defined by indentations such as wells or by association to adhesive regions on the support, among other methods. The microparticles may be touching or they may be separated so that individual microparticles are not touching. In many aspects, populations of microparticles for detection of a single target may be encoded with a single code indicative of that target while other populations may be labeled with a code for another target, even though each microparticle in the population may be specific for a different label-tag.

FIG. 2C illustrates another method for detection and counting of the number of label-tags and thus the number of individual targets. As above the label-tags, L1, L2, L3 and L4 are attached to the copies of a target 203 to form target-label-tag molecules 205. The target-label-tag molecules are then subjected to PCR amplification in individual reactions, each having a single primer pair that includes a first target specific primer “TS” and a label-tag specific primer, “L1”, “L2”, “L3” or “L4” in the figure. The “TS” primer is the same for each reaction because a single target is being interrogated. The L1-L4 primers are different for each reaction. Each target-label-tag combination that is present after ligation will result in an amplification product in the reaction that includes the corresponding label-tag specific primer (indicated by “YES” in the figure). Each label-tag that isn't selected (L3) will result in no amplification (indicated by “NO” in the figure). The amplification products can be detected by any method available, including real time PCR or end point PCR where products are separated according to size.

The label-tags may be attached to the targets through any of a variety of mechanisms. Examples for methods for attachment of label-tags to targets are provided herein. Attachment may be, for example, by extension of a primer that has a label-tag portion and a target specific portion. The target specific portion may be specific for a single target, for example, a locus specific primer, or it may be specific for a class of targets, for example, an oligo dT region. Extension may be polymerase mediated, e.g. DNA or RNA polymerase, and may be template mediated (where the target serves as template for extension of the primer) or template independent. For template mediated extension the template may be RNA or DNA or an RNA:DNA chimera. The primer may be RNA or DNA or an RNA:DNA chimera (see, for example, U.S. Pat. No. 6,251,639 which is incorporated herein by reference). The primer may also include modified bases such as locked nucleic acids (LNAs), peptide nucleic acids (PNAs), inosines, isoC, isoG, or the like. In some aspects label-tags may be attached by ligation using RNA or DNA ligase that may be heat labile or heat stabile.

In one aspect, the targets are small RNAs that are not polyadenylated. To attach identifiers to these small RNAs a first pool of identifier primers may be used to generate labeled cDNA product. The identifier primers may have (in the 5′ to 3′ direction) a common priming sequence, an identifier region and a target specific region that is complementary to a first region in the small RNA. The priming sequence and the target specific region are common in all identifier primers in the pool and the identifier region varies. The primers are hybridized to the targets and extended using a reverse transcriptase. This generates an identifiable cDNA for each small RNA target occurrence. The pool of cDNAs can be amplified using a primer specific for the small RNA target and a common primer complementary to the common priming sequence. The amplification products can be analyzed to determine how many different identifiers are included in the amplification product. The pool of cDNAs can also be analyzed by performing separate PCR amplifications for each identifier in the pool as illustrated in FIG. 2C. The reactions may include a primer for one of the identifiers and a primer for the target. A separate reaction is used for each identifier so if the pool has 1,000 different identifiers the analysis may include 1,000 different amplification reactions, although a subset may be analyzed, for example, reactions may be performed for more than 90% of the identifiers, more than 80% or more than 50%. Each reaction may be analyzed for the presence or absence of an amplification product where the number of “present” calls indicates the number of occurrences of the target in the sample. Methods for performing many individual amplification reactions by PCR are disclosed, for example, in Heyries et al. Nature Methods 8, 649-651 (2011), which is incorporated herein by reference. Methods for Digital PCR may be used but the partitioning step may be omitted since each reaction is specific for a single identifier. The reactions may be run in micro well plates, capillaries, arrays or miniaturized chambers, or on localized features of an array, e.g. arrays or beads. In some aspects each feature of an array has a different identifier primer attached to the array and an amplification reaction is performed using that primer and a common primer that may be complementary to a specific target to be counted. The common primer may be in solution or it may be attached to all of the features of an array for detection of a specific target.

FIG. 3 shows a schematic of one method for attachment of label-tags to fragments of DNA. The nucleic acid target 301, which may be genomic DNA, has fragmentation sites, for example, restriction sites, indicated as vertical lines 303. The target 301 is fragmented to generate fragments 305. Fragmentation may be site specific, e.g. restriction sites, or non-specific, e.g. by shearing or sonication. Adaptors that preferably contain label-tags 306 are ligated to the fragments to generate adaptor-ligated fragments 307. The adaptors may ligate to all fragments. The adaptor-ligated fragments can be circularized to generate circles 309 that include the two label-tag containing adaptors ligated together 311 and the fragment 305. The circularized fragments can be treated with exonuclease to remove unligated fragments. Target specific primer pair 313 can be used to amplify fragment 314. In some aspects the circles are linearized prior to amplification (after exonuclease treatment if it is used) by cleavage within fragment 305, preferably at a position between the sites of binding of the primers of the primer pair 313 to facilitate amplification. During amplification non-target circles will be amplified poorly or not at all because the primers in primer pair 313 are not complementary to the non-targets. The PCR product has the label-tag region 311 flanked by target specific regions. Counting of the targets is by detection of the junction sequences 315 and/or 317. Detection may be, for example, by sequencing through the junction or by hybridization to a probe complementary to the junction. If an array is used, the array probe is preferably complementary to the junction between the target specific region and the label. The two such junctions 315 and 317 in the PCR product could each be targeted on either strand (since the product is double stranded). The products may be fragmented, labeled and hybridized to an array of probes to the junctions. The label-target combination can be hybridized to an array for counting.

The methods disclosed herein and the examples below demonstrate that a population of indistinguishable molecules can be stochastically expanded to a population of uniquely identifiable and countable molecules. High-sensitivity threshold detection of single molecules is demonstrated, and the process can be used to count both the absolute and relative number of molecules in a sample. The method should be well suited for determining the absolute number of multiple target molecules in a specified container, for example in high-sensitivity clinical assays, or for determining the number of transcripts in single cells. The approach should also be compatible with other molecular assay systems. For example, antibodies could be stochastically labeled with DNA fragments and those that bind antigen harvested. After amplification, the number of label-tags detected will reflect the original number of antigens in solutions. In the examples shown here, DNA is used because of the great diversity of sequences available, and because it is easily detectable. In principle, any molecular label-tag could be used, for example fluorescent groups or mass spectroscopy tags, as long as they are easily detected and they have sufficient diversity for the desired application. Although many of the examples refer to populations

It is instructive to contrast the attributes of stochastic labeling with other quantitative methods. Microarray and sequencing technologies are commonly used to obtain relative abundance of multiple targets in a sample. In the case of microarray analysis, intensity values reflect the relative amount of hybridization bound target and can be used to compare to the intensity of other targets in the sample. In the case of sequencing, the relative number of times a sequence is found is compared to the number of times other sequences are found. Although the techniques differ by using intensity in one case and a digital count in the other, they both provide relative comparisons of the number of molecules in solution. In order to obtain absolute numbers, quantitative capture of all sequences would need to be assured; however in practice the efficiency of capture with microarray and sequencing technologies is unknown.

Unlike the stochastic labeling methods disclosed herein, digital PCR confers uniqueness by partitioning into unique containers. Digital PCR is an absolute counting method where solutions are stochastically partitioned into multi-well containers until there is an average probability of one molecule per two containers, then detected by PCR. This condition is satisfied when, P₀=(1−e^(−n/c))=½; where n is the number of molecules and c is the number of containers, or n/c is 0.693. Quantitative partitioning is assumed, and the dynamic range is governed by the number of containers available for stochastic separation. Once the molecules are partitioned, high efficiency PCR detection gives the yes/no answer and absolute counting enabled. To vary dynamic range, micro-fabrication can be used to substantially increase the number of containers. Similarly, in stochastic labeling, the same statistical conditions are met when P₀=(1−e^(−n/m))=½; where m is the number of label-tags, and one half of the label-tags will be used at least once when n/m=0.693. The dynamic range is governed by the number of label-tags used, and the number of label-tags can be easily increased to extend the dynamic range. The number of containers in digital PCR plays the same role as the number of label-tags in stochastic labeling and by substituting containers for label-tags we can write identical statistical equations. Using the principles of physical separation, digital PCR stochastically expands identical molecules into physical space, whereas the principle governing stochastic labeling is identity based and expands identical molecules into identity space.

In preferred aspects, of the presently disclosed methods, a diverse set of label-tags is randomly attached to a population of identical molecules and the population of identical molecules is thereby converted into a population of distinct molecules suitable for threshold detection. Random attachment as used herein refers to a process whereby any label-tag can be attached to a given molecule with the same probability. To demonstrate stochastic labeling methods experimentally the absolute and relative number of selected genes were determined after stochastically labeling 360,000 different fragments of the human genome. The approach does not require the physical separation of molecules and may take advantage of highly parallel methods such as microarray and sequencing technologies to simultaneously count absolute numbers of multiple targets. In some embodiments, stochastic labeling may be used for determining the absolute number of RNA or DNA molecules within single cells.

The methods disclosed herein may be used to take quantitative measurements of copies of identical molecules in a solution by transformation of the information to a digital process for detecting the presence of different label-tags. The stochastic properties of the method have been measured, and the relative and absolute digital counting of nucleic acid molecules is demonstrated. The method is extremely sensitive, quantitative, and can be multiplexed to high levels. In some aspects a microarray-based detection method is used, but the method is extendable to many other detection formats.

Methods for analyzing genomic information often utilize a correlation between a measurement of the amount of material associated with a location. The location can be, for example, a feature of an array that contains a specific sequence that is known or can be determined or any type of solid support such as a bead, particle, membrane, etc. A common aspect to these methods is often hybridization of a target to be measured to a complementary probe attached to the solid support. The probe may be, for example, an oligonucleotide of known or determinable sequence, but may also be BACs, PACs, or PCR amplicons.

Methods that use signal intensity to estimate relative concentrations of targets typically label the targets with a detectable label, often after an amplification step, and through hybridization of the detectably labeled target to the probe, the probe and thus the feature is also labeled. The amount of label-tag is detected and correlated with a measurement of the amount of target in the sample. The estimate of amount of a given target in a sample is typically relative to other targets in the sample or to previously obtained measurements and may be based on comparison to targets present in the sample at known or expected levels or to controls within the sample. This type of analysis can and has been used successfully, for example, to estimate genomic copy number to detect copy number variation in individuals or in cell populations (see, for example, Pinkel and Albertson, Annu. Rev. Genomics Hum. Genet. 6, 331-354 (2005), Lucito et al. Genome Res. 13, 229102305 (2004), Sebat et al. Science 305, 525-528 (2004), Zhou et al., Nat. Biotechnol. 19, 78-81 (2001) and Zhao et al. Cancer Res. 65, 5561-5570 (2005) and US Patent Pub. Nos. 20040157243 and 20060035258) or to estimate gene expression levels (see, for example, Lockhart et al., Nat. Biotechnol. 14:1675-1680 (1996), and Wodicka et al., Nat. Biotechnol. 15:1359-1367 (1997)).

Correlating intensity of hybridization signal or signal intensity with concentration of target molecules has limitations and can typically provide only an estimate of the absolute amount of a target, and may not be an accurate count of the actual amount of target present. The estimate may be an under or over estimate, particularly when comparing different targets or different samples. This is the result of many different factors, including but not limited to, differences between probes, feature specific effects, sample specific effects, feature size (as it decreases the ability to correlate accurately decreases) and experimental variation. Much of this variation can be addressed by data analysis methods, but the methods do not provide counting of individual molecules or events and are therefore subject to estimation errors.

Because of the density of different features that can be obtained using synthesis methods such as photolithography, microarrays can be applied to high density applications. For example, at feature sizes of 1 micron square an array can have about 10⁸ features per cm². Array densities that are currently commercially available include feature sizes of between 4×4 microns to 10×10 microns or feature spacing (distance between the centers of neighboring features of about 4 to about 10 microns). Within a feature, depending on the chemistry used for synthesis, the probes may be spaced typically at about 10 nm spacing resulting in about 10⁴ molecules in a 1×1 micron feature. At approximately full saturation about 10% of those probes are hybridized with target (with some photolithographic synthesis methods some portion of the probes are not full length and may not participate in specific hybridization to the target). Assuming that only about 80% of the size of the feature is being analyzed (to mitigate for overlap between features at the edge) there are only about ˜800 nm² functional area for the probe so about 640 functional molecules in an array having 1 micron² spacing between features. This relatively small number of functional molecules in a feature limits the dynamic range for estimating relative concentration from hybridization signal intensity. The methods disclosed herein do not require estimation of relative concentration; rather it is sufficient to have a binary readout that is not quantitative with respect to feature intensity. The dynamic range limitations observed with small feature sizes and small numbers of molecules on the array surface, are mitigated by the disclosed methods by using a counting or digital readout as a substitute for the typical analog signal resulting from array hybridization.

In further aspects a different label-tag sequence is attached to each molecule of a particular target sequence or more preferably a collection of target sequences of interest. To achieve unique or nearly unique labeling of targets the number of different label-tags to be attached to the targets should exceed the number of targets. For example, a sample having 100 molecules of target type 1 may be mixed with an excess of about 1000 different-identity label-tag sequences, forming a library of label-tag sequences. Multiple copies of the library of label-tag sequences are used so there are many copies of each different-identity label-tag. Different label-tag sequences from the library are appended to each of the 100 target molecules so that each of the 100 molecules of the first target sequence has a unique label-tag sequence appended thereto. This results in 100 different target-label-tag combinations that are each unique. The target-label-tag molecules may then be amplified to enrich the target-label-tag products relative to other non-targets. Amplification after labeling alters the absolute amount of the target, but because each occurrence in the original sample has been uniquely labeled this will not alter the count. The amplified target-label-tag products, whether amplified or not, can then be labeled with a detectable label like biotin, and hybridized to an array of probes or detected by other means.

If an array is used for detection, the features of the array that have target-label-tag hybridized thereto can be detected, for example, by labeling the hybridization complex with a fluorescent label-tag and detecting the presence of signal at the features. In this example, because there are 1000 different label-tags possible and a single target being analyzed, there are 1000 different possible label-target sequences that might be generated so an array having a different feature for each of the 1000 different possibilities can be used. Assuming each target is labeled and no label-tag is used twice, 100 of the 1000 different features should be detectable, indicating the corresponding label-tag has been used. A simple detector having m elements for each target sequence can be constructed. An array having 10⁸ features or elements could assay 10⁵ different targets using 10³ different label-tags, for example. Other detection methods do not require individual elements for each counter, for example, sequencing.

The number of different-identity label-tags that are needed depends upon the maximum number of expected targets and the requirement for accuracy in the count. Consider 1 copy of a target molecule in solution identified as t₁ reacted against a set of 10 label-tags, L_(m)={l₁, l₂, . . . l₁₀}. Each label-tag has a 0.1 probability of being chosen. Next consider multiple copies of the target, t_(n), reacted against the set of L_(m) (assume a non-depleting reservoir of label-tags). For simplicity, consider 3 copies of t: t₁, t₂ and t₃. Target t₁ will choose a label-tag, t₂ has a 0.9 probability of choosing a different label-tag, t₃ has a predictable probability of choosing the same label-tag as t₁ or t₂. For n copies choosing from m label-tags, outcomes can be modeled by the binomial distribution as discussed above. For 3 targets and 10 label-tags, the probability of a label-tag not being chosen, P₀ is (1−(1/10))³=0.729. The probability P₁ of being chosen exactly once is (3/10)(1−(1/10))²=0.243. The probability of being chosen twice, P₂ is 0.027 and the probability P₃ of being chosen 3 times is 0.001. Since P₀ is the probability of not being chosen, 1−P₀ is the probability of being chosen at least once. We define k=m(1−P₀) as the number of label-tags we expect to see in an experiment. Conversely, if we know m, and observe k we can solve for the number of molecules. In the previous example where n=3 and m=10 we expect to see 10(1−P₀) or 2.71 label-tags as our most probable outcome. Increasing m dramatically increases the counting efficiency, accuracy and dynamic range, e.g. for m=1,000, k(number of label-tags expected for n=10, k=9.96, for n=20, k=19.8. However, it may be desirable to use a lower number of label-tags to reduce cost and complexity of the analysis with the understanding that there is an increased probability of undercounting because label-tags are used multiple times for the same target.

In some aspects the pool of label-tags has approximately the same numbers of copies of each label-tag in the library. The label-tag sequences are not target specific, but may be similar to the tags that have been used for other tagging applications, for example, the Affymetrix GENFLEX tag array. The label-tags in a pool may be a collection of random sequences, such as a pool of N₆, N₇, N₈, N₉ or N₁₀, or mixtures of these lengths, where N can be any of the four bases. Preferably all label-tags in a set of label-tags will have similar hybridization characteristics so that the label-tags of the set can be detected under similar conditions. In some aspects the pool of label-tags has similar amounts of each tag, for example, within 2 fold or within 10 fold. In other aspects some label-tags may be present at high amounts relative to other label-tags. For example, some label-tags may be at high concentration in the pool, and others low, for example at a ratio of 100 to 1 or 1000 to 1.

In some aspects, the label-tag is attached without requirement for it to hybridize to any portion of the target so there is no or minimal bias as to which label-tag sequence is attached. In one embodiment, the label-tag is attached by ligation of the label-tag to one of the ends of the target. When array hybridization is used for detection the probes of the array may be complementary to a predicted junction between target and label-tag so it is preferable that the label-tags are attached to all occurrences of a target at the same position. This is facilitated if the termini of each occurrence of a selected target are the same and are known. This may be how the target exists in the unprocessed sample, for example for small RNAs that have defined and known ends such as miRNAs, siRNAs and other non-coding and structural RNAs or known ends can be generated in a target by cleavage at a specific site of known sequence. Such cleavage can be enzymatic, for example site specific restriction digestion or at a site that is targeted by hybridization of an oligo to facilitate cleavage by RNaseH or by an enzyme that has flap endonuclease activity such as FEN 1 or Taq DNA polymerase.

In another aspect the label-tag may be attached as a partially double stranded adaptor. One strand of the adaptor may serve as a splint to bring the target and the label-tag sequence together for ligation. The splint may include a first region that is complementary to one end of the target and a second region that is complementary to at least a portion of the oligonucleotide that carries the label-tag. The splint hybridizes to both target and label-tag oligo and brings the ends together for ligation by a ligase enzyme. In some aspects if there is a gap between the two it can be filled by extension of one or the other or by ligation of a gap filling sequence into the gap.

To facilitate amplification, adaptors may contain a universal or common priming sequence that is 5′ of the label-tag sequence. Attachment of universal or common primers to either end of a target can be followed by PCR amplification. The universal primers may be added along with the label-tag or at a subsequent ligation step or primer extension step.

For RNA targets an RNA ligase, such as T4 RNA ligase may be used. T4 RNA ligase 1 catalyses the ligation of a 5′ phosphoryl-terminated nucleic acid donor to a 3′ hydroxyl-terminated nucleic acid acceptor. Substrates include single-stranded RNA and DNA. See, for example, Romaniuk, P. and Uhlenbeck, O. (1983) R. Wu, L. Grossman and K. Moldave (Eds.), Methods Enzymol., 100, pp. 52-56. New York: Academic Press and Moore, M. J. and Sharp, P. A. (1992) Science, 256, 992-997. RNA targets may also be circularized and used as template for rolling circle amplification using an enzyme having reverse transcriptase activity. T4 RNA ligase 1 may be used for circularization of RNA by ligating the ends of the molecule together. T4 RNA ligase 1 can also be used to ligate RNA to DNA.

Full-length mRNA can be selected by treating total or poly(A) RNA with calf intestinal phosphatase (CIP) to remove the 5′ phosphate from all molecules which contain free 5′ phosphates (e.g. ribosomal RNA, fragmented mRNA, tRNA and genomic DNA). Full-length mRNAs are not affected. The RNA can then be treated with tobacco acid pyrophosphatase (TAP) to remove the cap structure from the full-length mRNA leaving a 5′-monophosphate. A synthetic RNA adapter can be ligated to the RNA population. Only molecules containing a 5′-phosphate, (i.e. the uncapped, full-length mRNAs) will ligate to the adapters. Preferably the adapter has a variable label-tag sequence, and may also have a constant sequence for priming. Preferably, the constant sequence is 5′ of the variable sequence. In some aspects, the adapter ligated mRNA may then be copied to form a first strand cDNA by, for example, random priming or priming using oligo dT. The cDNA may subsequently be amplified by, for example, PCR._T4 RNA ligase may also be used for ligation of a DNA oligo to single stranded DNA. See, for example, Troutt et al., (1992) Proc. Natl, Acad. Sci. USA, 89, 9823-9825.

In other aspects, the ligated target-label-tag molecule may be enriched in the sample relative to other nucleic acids or other molecules. This enrichment may be, for example, by preferentially amplifying the target-label-tag methods, using for example, a DNA or RNA polymerase, or by degrading non target-label-tag molecules preferentially.

In one aspect, the target-label-tag molecule may be nuclease resistant while the unligated target and unligated label-tag molecules may be nuclease sensitive. A nuclease can be added to the sample after ligation so that ligated target-label-tag molecules are not digested but non-ligated molecules are digested. For example, the targets may be resistant to a 5′ exonuclease (but not a 3′ exonuclease) while the label-tags are resistant to a 3′ exonuclease but not a 5′ exonuclease. Ligating target to label-tag generates a molecule that is resistant to 5′ and 3′ exonuclease activity. After ligation the sample may be treated with a 5′ exonuclease activity, a 3′ exonuclease activity or both 5′ and 3′ exonuclease activities. For examples of nucleases see Rittie and Perbal, J. Cell Commun. Signal. (2008) 2:25-45, which is incorporated by reference (in particular see Table 5). Exo VII, for example degrades single stranded DNA from both the 5′ and 3′ ends so the sample could be treated with Exo VII after ligation to degrade molecules that are not ligation products.

In another aspect amplification may include a rolling circle amplification (RCA) step. See for example, Baner et al. (1998) NAR 26:5073, Lizardi et al. (1998) Nat. Genet. 19:225, Fire and Xu, (1995) PNAS 92:4641-5, Zhao et al. Angew Chem Int Ed Engl. 2008; 47:6330-6337 and Nilsson et al. (2008), Trends in Biotechnology, 24:83-88. The targets may be ligated so that they have a label-tag and a universal priming (UP) sequence attached to the 5′ end of the targets. The UP-label-target is then ligated to form a circle. A primer complementary to the UP is then hybridized to the circles and extended using a strand displacing polymerase. The resulting amplification product contains multiple copies of the complement of the circle, UP-target-L.

In another aspect, targets may be labeled in a copying step. For example, a primer having a 3′ target specific region and a 5′ variable label-tag region may be hybridized to the targets, either RNA or DNA, and extended to create a single complimentary copy of the target. Each extension product will have a different label-tag and the junction between the label-tag and the target specific region is known. The target specific region may be common to multiple targets, for example, if the targets are mRNA the target specific region may be oligo dT. Polyadenylated mRNA may optionally be enriched by binding to oligo dT coated beads. The oligo dT region hybridizes to the polyA tail at the 3′ end of the mRNA and serves as a primer. The label-tag is 5′ of the oligo dT region and thus becomes part of the cDNA extension product. There is preferably an amplification primer sequence 5′ of the label-tag region that also becomes part of the extension product and can be used in a subsequent amplification step. In preferred aspects the cDNA extension product is made double stranded in a subsequent step. A second strand cDNA can be synthesized, for example, in the presence of RNaseH and a DNA polymerase. The amplification primer may be, for example, a promoter sequence for an RNA polymerase such as T7 or SP6 or variants thereof. Multiple labeled aRNA copies can be generated by IVT. In other aspects the amplification primer may include a recognition site for a nicking enzyme, such as Nt.BspQ1. The dsDNA can be nicked and the nick extended to create another copy and displacing the earlier copy in a strand displacing amplification step. The resulting amplified product in all cases can then be analyzed to detect the label-tag and enough of the target sequence to identify the target.

In another aspect the target specific region may be a short stretch of random sequence, e.g. N₆-label-tag. The extension may be performed in the presence of nuclease resistant nucleotides so that the extension product is resistant to nuclease but the unextended primers are not. After extension the reaction is treated with a 3′-5′ exonuclease activity to digest unextended primer. Exonuclease I, for example, removes nucleotides from single stranded DNA in the 3′ to 5′ direction and Exo III removes nucleotides from the 3′ termini of duplex DNA. Exonuclease T (or RNase T) is a single-stranded RNA or DNA specific nuclease that requires a free 3′ terminus and removes nucleotides in the 3′ to 5′ direction. The extension products are then detected by hybridization to probes that are complementary to the primers and include the unique label-tag portion and the constant target specific portion. If the target is RNA it can be digested with RNase H after extension. The extension product may also be amplified before hybridization.

FIG. 4 shows a strategy for selecting probes for target fragments. Each of these junction regions as shown has a counter region 411 denoted by N's, a fixed sequence 413 that is defined by the restriction enzyme used for fragmentation and a target specific region 415. The region 415 is shown as N's but in preferred aspects it is a known or predictable sequence of the target that is adjacent to the selected restriction site and can be used to identify the target. In an array is used for detection the array probes may be complementary to at least a portion of 411, a portion of 415 and all of 413. For each target sequence-counter combination there are 4 different probes that could be included on the array, according to the 4 possible junctions 401, 403, 405 and 407. For example, if the targets are 10 loci from each of 4 chromosomes and 4 probes per fragment are included for 1200 different label-tags (1000 specific plus 200 non-specific) the array could have 192,000 total probes (4×10×4×1200). If sequencing is used for detection it is preferable to obtain sequence information for the region 411 and enough of region 415 to determine the identity of the target being sequenced. The length of 415 that need be determined will depend upon the number of different targets being analyzed and the complexity of the sample being analyzed, e.g. the fewer possible targets the less sequence needed to make an identification.

In some aspects methods for selecting a collection of label-tags optimized for use in the disclosed methods is contemplated. For example, a list of all possible 14 mers may be used as a starting pool (4¹⁴ is ˜268 million different sequences). Different label-tag lengths can be used resulting in different numbers of starting sequences. Once a list of starting sequences has been generated, that list may be processed using one or more of the following steps: eliminate all label-tags that are not at least 50% GC content; eliminate all label-tags that do not use each of the 4 possible nucleotides at least twice; eliminate all label-tags that have more than two Gs or Cs in tandem, e.g. a probe with GGG or CCC would be eliminated, or with more than three As or Ts in tandem, e.g. AAAA or TTTT would be removed; remove label-tags that contain a selected restriction site; remove label-tags having a Tm that is outside of a range (for example 38.5 to 39.5° C., 38 to 40° C., 38-39° C., or 39-40° C.); and remove probes that have self complementarity beyond a selected threshold. Further processing steps may include: perform a hierarchical clustering to maximize sequence differences between label-tags to minimize cross hybridization, same label-tag to same probe and minimize self-complementarity within the collection to reduce tendency of two label-tags binding to each other.

FIG. 5 shows a counter adaptor 501 that includes a counter region 505, a constant region for priming 503 and a sticky end 507 for ligation to an overhang created, in the fragments, by restriction digestion of the sample, for example with BamHI. In step 5001 adaptors 501 are ligated to target fragments 509. After ligation of the adaptors 501 to the target fragment 509 there are typically two adaptors ligated to the target fragment, one at either end. It is probable that the counters on the two ends will be different, as shown, although there is a predictable probability of having the same counter ligated to both ends of the same fragment. After adaptor ligation the adaptor-ligated fragments 511 can be amplified in step 5002 by PCR using a common primer to the 503 region of the adaptor. The adaptor may first be filled in to make it double stranded using a DNA polymerase. The PCR amplification may be used to preferentially amplify fragments of a selected size range, for example, 300 to 2 kb. Smaller fragments are not amplified as efficiently because of self complementarity between the ends of the individual strands (capable of forming a panhandle structure that inhibits amplification) and longer fragments (longer than about 3 kb) also don't amplify well. For a discussion of one-primer multiplex PCR see, for example, Matsuzaki et al. Genome Res. 2004, 14(3):414-425, which is incorporated herein by reference in its entirety.

The PCR product 511 may be circularized by ligating the adaptor ends together at circularization point 515. After circularization, the uncircularized fragments can be digested using an exonuclease, for example. The circularized fragments can be amplified using target specific primers to generate amplification product 513. Step 5002 includes formation of the circularized product (not shown) followed by PCR amplification to generate product 513. In FIG. 5 the target specific primers are identified as “TS primer F” and “TS primer R”. They are primers that are specific for the target sequences being counted. Whereas the primers used to amplify 511 are common to all adaptor ligated fragments and will amplify all fragments that are in the size range to be amplified using PCR, the TS primers are specific for selected targets to be analyzed and this amplification step will reduce the complexity of the sample by preferentially amplifying the targets to be counted. Non-targets are amplified in step 5001 but not efficiently in step 5002. The amplification product 513 has in the 5′ to 3′ direction, target specific sequence, overhang sequence, a first counter “L₁”, first adaptor sequence, circularization junction 515, second adaptor sequence, second counter “L₂”, second overhang sequence and a second target specific sequence. The first and second counter are generally different (although they may be the same at a low probability depending on the number of species of counters) and the first and second target sequence are different. The product 513 or preferably fragments thereof can be detected by a variety of methods, for example, an array of probes as exemplified by probe 517 can be used or the product can be sequenced using any available method. As shown in FIG. 5 step 5003, the array probe 517 is complementary to a region of the target, the overhang region and the counter. When hybridized the target will have an overhanging single stranded region that corresponds to the adaptor sequence. A labeled probe 519 that is complementary to one strand of the adaptor can be hybridized and the ligated to the array probe as shown in step 8004, and as described below. The labeling of the array probe with biotin indicates the presence of that target-counter L₁ combination and is indicative of the presence of one occurrence of the target. The array has probes (probe features comprising multiple copies of the sample probe sequence) for each possible target-counter combination.

In some aspects the label-tags are generated within the target to be counted. For example, the label-tag may be a unique cleavage site in a target fragment as shown in FIG. 6. Each of the copies of the target to be counted 601 have a common sequence at one end identified in the figure as 603. This may be a common sequence that has been added to the targets through ligation or primer extension or it may be a naturally occurring sequence in the target. The targets are fragmented randomly, for example by shearing or sonication resulting in cleavage at the points indicated by the arrows to generate cleavage products 604. Cleavage is at a different and unique site in each of the fragments and results in a unique sequence in the target immediately to the left of the point of cleavage in the illustration (indicated by circles in fragments 607). This unique sequence can function as a label-tag for the disclosed methods. A second common sequence 605 may be attached to each of the targets immediately downstream of the cleavage point, through for example ligation of an adaptor sequence. The resulting targets 607 can be analyzed directly to determine how many unique sequences are present and using this number as an indication of the number of targets in the starting sample. This is illustrated for nucleic acids, but could similarly be applied to proteins or other contiguous strings of monomers or units that are assembled in a non repeating pattern.

An exemplary method for detection is diagramed in FIG. 7. The 3840 distinct label-tag oligos (counters) were single stranded oligos pooled from the Dde1 TACL primer panel (40 primer plates by 96 wells per plate for 3840 different oligos). An example label-tag oligo 701 is shown: (SEQ ID NO: 1964) 5′TCGATGGTTTGGCGCGCCGGTAGTTTGAACCATCCAT-3′. The 48 different primers used as “targets” were synthesized using as target 48 different 21 nucleotide sequences from the Affymetrix TrueTag 5K_A array. An example target oligo 707 is shown (SEQ ID NO: 1965) 5′GCCATTTACAAACTAGGTATTAATCGATCCTGCATGCC-3′.

The “label” or “counter” oligo has an 18 nt common sequence at the 5′ end and a 15-28 nt “label” (or “counter”) sequence at the 3′ end. An example “label” 705 is shown. The universal primer 703 common to all or a group of the label-tag oligos has sequence 5′ TCGATGGTTTGGCGCGCC-3′ (SEQ ID NO: 1966) at the 5′ end and each target oligonucleotide has common sequence 711 that is 5′ AATCGATCCTGCATGCCA-3′ (SEQ ID NO: 1967) at the 3′ end as universal priming sequence. The target oligos vary in sequence at the 5′ ends 709.

In another embodiment, illustrated schematically in FIG. 8, genomic DNA 301 is fragmented with a restriction enzyme, for example, BamHI, which generates a single stranded overhang for sticky ended ligation. The fragments 305 are ligated to adaptors 501 that include a label-tag 505 and a universal priming site 503. Different adaptors vary in the label-tag portion 505 but have a common priming site 503. The label-tag is 3′ of the universal priming site so that it is between the fragment and the universal priming site. The adaptor ligated fragments are amplified by PCR using primer 313. The PCR product can be fragmented, labeled with a detectable label and hybridized to an array. The resulting strands are detected by hybridization to an array having target-label-tag probes to the junction between target and label-tag as illustrated in FIG. 7. The array may have a different probe feature for each target-label-tag combination. The figure shows a collection of features for each of Target 1 and Target 2 where each different probe feature is represented by a single vertical line. The PCR amplicons may be fragmented prior to array hybridization. Preferably the fragments are labeled, for example, by TdT incorporation of a nucleotide that can be detected, such as a biotin containing nucleotide.

The probes of the array are complementary to the junction between the label-tag and the restriction fragment. The sequences at the ends of the individual strands of the restriction fragments are predicted based on in silico digestion of the human genome. Also, fragments are targeted that are within the size range that is known to amplify efficiently by adaptor ligation PCR, for example, 200 bases to 2 kb. The adaptor 501 has two segments, a constant priming region 503 and a variable label-tag region 505. Together 503 and 505 form the label-tag adaptor 501. The primer 313 has the same sequence 5′ to 3′ as 503. The schematic is drawn showing only one strand, but one of skill in the art would understand that in a preferred embodiment the genomic DNA is double stranded and the restriction fragments have two strands, which may be referred to as a top strand and a bottom strand. The convention is that the top strand is drawn 5′ to 3′ left to right and the bottom strand is the complement of the top strand and is drawn 3′ to 5′ left to right. Adaptors are preferably double stranded for at least a portion of the adaptor. They may have single stranded overhangs, for example to have “sticky ends” that facilitate hybridization and ligation to the overhang resulting from restriction digestion. In a preferred aspect, the same adaptor can be ligated to the two ends of a strand of a restriction fragment and may be ligated to one or both strands. The adaptor may be ligated to the ends of the top strand in opposite orientations as shown in FIG. 8, so that the label-tag 505 is internal to the priming site at both ends. The adaptor may have a top and a bottom strand and the top strand may be ligated to the top strand of the fragment and the bottom strand ligated to the bottom strand of the fragment. The top and bottom strands of the adaptor may be complementary over the entire length, but often have single stranded regions at one end to facilitate sticky ended ligation to an overhang created by a restriction enzyme.

FIG. 9 shows a method for reading out the counter-labeled targets on arrays by ligation of biotin-labeled oligos 901 to the array probes if the cognate counter-labeled targets are present. The left panel shows the results when target region G₁ ligated to label-tag L₁ to form G₁L1 hybridizes to the complementary G₁L1 probe on the array. The constant region (in white) can hybridize to its labeled complement so that the 3′ end of the biotin-labeled oligo is juxtaposed with the 5′ end of the L₁ region of the probe on the array and the ends can be ligated to label-tag the array probe. In the center panel the target hybridizing to the G₁L1 probe is non-cognate; the label-tag region is L₂ and not L₁ so it does not hybridize to the L₁ region of the probe. The biotin-labeled oligo can hybridize to the partially hybridized target but it is not juxtaposed with the 5′ end of the L₁ region of the probe so it should not ligate to the probe. In the right panel the target shown hybridized has the L₁ region and is complementary to the array probe at that region, but the array probe has a G region that is not G₁ so the G₁L1 target does not hybridize. The labeled oligo can hybridize to the target but because the L₁:L₁ region is short the duplex is not stable and the labeled oligo does not ligate to the end of the array probe efficiently. This allows for labeling of properly hybridized target-label-tag pairs with both hybridization and ligation discrimination.

In the collection of label-tag sequences, each label-tag species has a different sequence but multiple copies of each species are preferably present. All species may be present at the same amount or there may be variable amounts of some species, for example, some species may be present at 10 M and others at 1M. Other ratios are also possible, e.g. 1:100 or 1:1000 for species in the collection. It may be desirable to vary the relative ratios of species in the label-tag pool in accordance with the expected ratios of targets to be detected. In many aspects it is preferable that the number of different species of label-tags in the pool is at least 10 times the number of copies of the most abundant target to be counted. In a preferred aspect, the label-tags are a collection of known sequences such as a collection of all possible 6mers (N₆), (or 7-14mers) or a subset of all possible N-mers of a given length. Subsets may be selected to optimize or normalize hybridization conditions or to minimize cross hybridization. Sets of label-tags may be further subdivided into subsets of

In preferred aspects the label-tag sequences are covalently associated with the targets. Attachment, by for example, ligation, is random so that any given label-tag has about the same probability of ligating to any one target occurrence. So if there are 1000 different occurrences of a target each could be ligated to a different label-tag sequence and the probability that any two target occurrences will have the same label-tag ligated is preferably low and depends on the number of label-tags available. Because the attachment is a random stochastic process there is a known probability that if there are C copies of a given target and N different label-tags that any two copies of a target T will have the same label.

The relationship between the number of targets and the number of label-tags determines the probability that two C's will have the same L. In preferred aspects Y is greater than X for each target to be counted. This reduces the probability of undercounting due to double labeling. If C1 and C2 of T1 are both labeled with L3 both copies will be counted as a single occurrence, resulting in under counting. Undercounting can also be adjusted for by estimating the number of copies that are likely to be multiply labeled and adjusting the final count upwards to take those into account. For example, if there is a likelihood that 5 of 1000 copies will be labeled with the same label-tag then the final number should be adjusted up by 0.5%.

In preferred aspects, the detection is by hybridization to an array of probes. The array has a collection of features for each target that includes a different feature for each label-tag. For example, if there are X label-tags there are X features for each target, T1L1, T1L2, . . . T1LX and the same for target 2, T2L1, T2L2, . . . T2LX, out to TNL1, TNL2, . . . TNLX. The number of features of the array is on the order of X times N. Each probe has a target complementary sequence and a label-tag complementary sequence. Within a set of probes for a given target the target segment of the probe would remain constant and the label-tag portion varies from feature to feature so that each label-tag sequence is represented by at least one feature for each target.

In one aspect, the methods may be used to count the number of copies of each of a plurality of targets in a sample. The amount of target containing sample mixed with the label-tags may be diluted so that the number of copies of each target to be counted is less than the number of label-tags. For example, if the targets to be counted are present at about 1,000 copies per cell and there are 10,000 label-tags you want to have the amount of sample in the mixture to be about the equivalent of one cell's worth of RNA. You can mix that with multiple copies of each label-tag, but you want to keep the absolute number of copies of target below the number of types of label-tag sequences. Dilution of the sample and use of an appropriately small amount of starting material may be used. If a target sequence is present at low copy number per cell it is possible to use the nucleic acid from a larger number of cells. For example, to measure the DNA copy number of a chromosomal region relative to other chromosomal regions the expected copy number is low (e.g. 2 for normal) so if there are 10,000 different label-tags, the number of genomes that can be added to the sample for attachment of label-tags can be high, e.g. 500 to 1000.

In one aspect, the methods are used to identify regions of genomic amplification and chromosomal abnormalities. For example, the methods may be used to detect trisomy or other forms of aneuploidy. Trisomy is a type of aneuploidy where most of the chromosomal regions will be present in 2 copies per cell and the region of trisomy will be present in 3 copies per cell. Trisomy may also be partial, i.e. there is an extra copy of part of a chromosome. Trisomy 21 and 18 are the most common in humans. Trisomy may be indicated if 3:2 ratio is observed in a counting analysis performed using the disclosed methods. For example, if the sample contains about 500 genomes the observed count may be 1000 copies of most regions and 1500 copies of the trisomy regions. Small errors in the counting, resulting from undercounting, would have little or no effect on the conclusion. In some aspects it may be desirable to detect aneuploidy in mixtures of samples, for example, mother and fetus.

In some aspects, controls of known copy number may be spiked in to a sample as an internal control or to determine accuracy.

Stochastic labeling of t_(1,N) (collection of essential identical molecules of copy 1, 2 . . . N of target 1) by L_(1,m) (effectively an infinite reservoir of diversity m when m is much greater than N). This allows for complete or near complete resolution of members of t_(1,N), by imparting separate identities to the members of the collection of t_(1,N) (provided that M is sufficiently smaller than N in the labeling). This provides for a stochastic or random projection of t_(1,N) onto L_(1,m). In some aspects L_(1,m) is a library and the members of the library that are associated with t_(1,N) can be counted to determine the number of copies of the target. In some aspects the methods can be described as indexing the members of the target. This provides a method to follow individual molecules that are members of a type of molecule that would not otherwise be distinguishable one from another.

Because stochastic labeling can impart identifiability to otherwise non-identifiable molecules it can impart identifiability to any two targets that may be very similar, but different. Examples of targets that may be highly similar but could be separately counted using the disclosed methods, include, for example, alternative splice forms of a gene, and sequences that have one or more variations, including a variation in a single base (e.g. SNP or indels (insertion or deletions of short regions, e.g. 1-5 bases). Counting alleles can be used to measure allelic ratios or mosaicism. For example, two populations of cells within the sample individual may have different genotypes resulting in different numbers of each allele of one or more SNPs. The methods allow for precise measurement of the numbers of copies of each allele of a given SNP in a sample. In some aspects the methods impart a clonal labeling, that allows a single copy to be separately detected and separately isolated from the solution. Variants that occur as the result of amplification after the label-tag has been attached, e.g. resulting from polymerase errors, can also be detected as they will have the same label-tag but different sequences.

Some nucleic acid sequencing reactions use methods that stochastically attach targets to a solid support followed by amplification of the attached target and analysis. The target attaches in an unknown location and the location can be determined by sequencing the amplified target at specific locations. In contrast, the disclosed methods provide for clonal amplification of known targets in a known location. The stochastic nature of the formation of the target-label-tag molecule provides a mechanism for isolating single occurrences of selected targets that can be subsequently amplified and analyzed. In some aspects the label-tag can be used as a handle for isolating clonal populations of targets. The labeling step generates an indexed library that has a variety of applications. For example, the indexed library could be used for sequencing applications. The method adds distinguishability to any set of molecules, even molecules that are not distinguishable by other mechanisms because they may share common regions or even been identical. The indexed library can be stored and used multiple times to generate samples for analysis. Some applications include, for example, genotyping polymorphisms, studying RNA processing, and selecting clonal representatives to do sequencing.

In some aspects the methods are used to stochastically label-tag a polyclonal antibody population. This may be used to identify different polyclonal populations.

The methods may be used to convert an analog readout of hybridization signal intensities on arrays into a measurable process that can be scored digitally on the arrays. The method leverages a random process where the tagging of assayed molecules is governed by stochastic behavior. In a random process, the more copies of a given target, the greater the probability of being tagged with multiple label-tags. A count of the number of incorporated label-tags for each target can approximate the abundance level of a given target of interest. The ability to count label-tags on microarrays would be a clear cost-advantage over the other existing techniques.

A stochastic counting assay system as described herein can also be a sub-system within a much larger bio-analysis system. The bio-analysis system could include all the aspects of sample preparation prior to, for example, optical detection, the post processing of data collected in the optical detection phase and finally decision making based on these results. Sample preparation may include steps such as: extraction of the sample from the tested subject (human, animal, plant environment etc.); separation of different parts of the sample to achieve higher concentration and purity of the molecules under investigation; sample amplification (e.g. through PCR); attachment of detectable labels to different parts of the sample; and transfer of the sample or a portion of the sample into a reaction vessel or site on a substrate. The post processing of the collected data may include: normalization; background and noise reduction; and statistical analysis such as averaging over repeated tests or correlation between different tests. The decision making may include: testing against a predefined set of rules and comparison to information stored in external data-bases.

The applications and uses of the stochastic labeling and counting methods and systems described herein can produce one or more result useful to diagnose a disease state of an individual, for example, a patient. In one embodiment, a method of diagnosing a disease comprises reviewing or analyzing data relating to the presence and/or the concentration level of a target in a sample. A conclusion based review or analysis of the data can be provided to a patient, a health care provider or a health care manager. In one embodiment the conclusion is based on the review or analysis of data regarding a disease diagnosis. It is envisioned that in another embodiment that providing a conclusion to a patient, a health care provider or a health care manager includes transmission of the data over a network.

Accordingly, business methods relating to the stochastic labeling and counting methods and methods related to use thereof as described herein are provided. One aspect of the invention is a business method comprising screening patient test samples for the amount of a biologically active analyte present in the sample to produce data regarding the analyte, collecting the analyte data, providing the analyte data to a patient, a health care provider or a health care manager for making a conclusion based on review or analysis of the data regarding a disease diagnosis or prognosis or to determine a treatment regimen. In one embodiment the conclusion is provided to a patient, a health care provider or a health care manager includes transmission of the data over a network.

Applications for the disclosed methods include diagnosing a cancerous condition or diagnosing viral, bacterial, and other pathological or nonpathological infections, as described in U.S. Pat. No. 5,800,992. Additional applications of the disclosed methods and systems include, pathogens detection and classification; chemical/biological warfare real-time detection; chemical concentration control; dangerous substance (e.g., gas, liquid) detection and alarm; sugar and insulin levels detection in diabetic patients; pregnancy testing; detection of viral and bacterial infectious diseases (e.g. AIDS, Bird Flu, SARS, West Nile virus); environmental pollution monitoring (e.g., water, air); and quality control in food processing.

Any available mechanism for detection of the label-tags may be used. While many of the embodiments discussed above use an array readout form, it will be obvious to one of skill in the art that other methods for readout may be used. For example, sequencing may be preferred in some embodiments, but detection may be by hybridization, PCR, real time PCR or reverse transcription, optionally followed by PCR. Amplification may be by PCR but may also be by any method of amplification available, such as random priming by a strand displacing polymerase.

In some aspects the readout is on an array. The array may be a solid support having immobilized nucleic acid probes attached to the surface in an ordered arrangement. The probes may be, for example, synthesized in situ on the support in known locations using photolithography or the probes may be spotted onto the support in an array format. As discussed above, in some embodiments the array includes a probe feature for each possible label-target combination. A feature preferably includes many copies of a single probe sequence. The feature may also have some probes that are not full length, resulting from truncation of synthesis. The photo activation process may not be 100% efficient so some probes are terminated at each step without having subsequent bases added. These truncated probes have the sequence of a portion of the full length probe.

In many aspects the detection of the unique label-tag-target molecules can be done by using a sequencing readout. It is necessary only to determine the sequence of enough of the label-tag to unambiguously distinguish between other label-tags in the pool used and enough of the target to unambiguously distinguish between other targets being analyzed. After attachment of the label-tags to the targets in a stochastic manner, the targets may be amplified according to any of the methods disclosed herein prior to sequencing analysis of the product. Amplification is not required for some sequencing methods that are capable of sequencing single molecules, for example, methods that sequence a molecule as it travels through a narrow opening or nanopore, the methods developed by Helicos and sequencing by synthesis in zero-mode wave-guides (Pacific Biosciences).

The methods of the invention can be used in conjunction with essentially any sequencing methodology. Suitable techniques include, for example, Pyrosequencing, FISSEQ (fluorescent in situ sequencing), MPSS (massively parallel signature sequencing) sequencing by ligation-based methods, sequencing by synthesis, sequencing by hybridization. Methods that uses arrays of chemical-sensitive field effect transistors, or FETs, to detect how nucleotides incorporate into growing strands of DNA by measuring changes in current or pH for sequencing may also be applied to the methods disclosed herein.

A number of alternative sequencing techniques have been developed and many are available commercially. For a review see, for example, Ansorge New Biotechnology 25(4):195-203 (2009), which is incorporated herein by reference. These include the use of microarrays of genetic material that can be manipulated so as to permit parallel detection of the ordering of nucleotides in a multitude of fragments of genetic material. The arrays typically include many sites formed or disposed on a substrate. Additional materials, typically single nucleotides or strands of nucleotides (oligonucleotides) are introduced and permitted or encouraged to bind to the template of genetic material to be sequenced, thereby selectively marking the template in a sequence dependent manner. Sequence information may then be gathered by imaging the sites. In certain current techniques, for example, each nucleotide type is tagged with a fluorescent tag or dye that permits analysis of the nucleotide attached at a particular site to be determined by analysis of image data. As indicated above, any method of sequencing that is available could be applied to detection of the target-label-tags to count the number of unique target-label tag combinations to count the number of a given target in a sample.

In another aspect, mass spec analysis may be used to detect the label-tags and count the targets. The label-tags can be distinguishable based on size or other property that can be detected. Many of the examples provided herein identify the label-tag based on unique nucleic acid sequence but any distinguishable label-tag may be used, for example, the pool of label-tags may be label-tags that are differentially detectable based on fluorescence emission at a unique wavelength.

FIG. 9 shows a method for reading out the labeled targets on arrays. On the left, the target with G₁ ligated to L₁, “G₁L1”, is shown hybridizing to the complementary array probe over the entire length of the probe. On the right target G₁ ligated to label-tag L₂ is shown partially hybridized to the G₁L1 probe on the array. On the left the biotin labeled constant segment can hybridize to the G₁L1 target and ligate to the 5′ end of the G₁L1 array probe. The constant segment can hybridize to the L₂ segment but will not ligate to L₁. This allows for labeling of properly hybridized target-label-tag pairs with both hybridization and ligation discrimination. The lower panel shows an example where the target or G portion is not matching with the probe on the array. This will not ligate efficiently because it hybridizes less stably.

The left panel shows the results when target G₁ ligated to label-tag L₁ to form G₁L1 hybridizes to the complementary G₁L1 probe on the array. The constant region (in white) can hybridize to its labeled complement so that the 3′ end of the labeled complement is juxtaposed with the 5′ end of the L₁ region of the probe on the array and the ends can be ligated. In the center panel the target hybridizing to the G₁L1 probe is non-cognate, the label-tag region is L₂ and not L₁ so it does not hybridize to the L₁ region of the probe. The labeled oligo can hybridize to the partially hybridized target but it is not juxtaposed with the 5′ end of the L₁ region of the probe so it should not ligate to the probe. In the right panel the target shown hybridized has the L₁ region and is complementary to the array probe at that region, but the array probe has a G region that is not G₁ so the G₁L1 target does not hybridize. The labeled oligo can hybridize to the target but because the L1:L1 region is short the duplex is not stable and the labeled oligo does not ligate to the end of the array probe.

The methods are broadly applicable to counting a population of molecules by performing a stochastic operation on the population to generate a stochastic population of identifiable molecules. The targets need not be identical. For example, the methods may be used to count the absolute number of members of a group. In one aspect, a sample having an unknown number of copies of a selected nucleic acid target is fragmented randomly so that on average each copy of the target has a different end resulting from a distinct fragmentation event. A common adaptor sequence can be ligated to the end of each fragment and used for amplification of the fragments. Each ligation event generates a new molecule having a junction formed by the end of the random fragment and the adaptor sequence. The new junction can be detected by, for example, sequencing using a primer complementary to the adaptor or a region of the adaptor. Because the fragmentation was a stochastic process the number of different ends detected is a count of the number of different starting target molecules, assuming one fragment per starting target molecule.

FIG. 26 shows another method for attaching label-tags. Polyadenylated RNA 4001 is reverse transcribed using a first primer [UR1_label] 4002. The primer may include several regions including an oligo dT region 4003 3′ of a label-tag region 4005. A sequencing primer region 4007 may be 5′ of the label-tag and another priming region 4008 may be 5′ of that. The primer region 4007 may be used as a first round sequencing primer. The reaction time can be controlled to shorten transcript length in the first round synthesis reaction. The primer preferably terminates at the 3′ end with at least one non-T base so that it can hybridize at the beginning of the polyA tail rather than at a random position within the tail. For example, if the primer has VN at the 3′ end (as shown in the figure) where V is A, C or G but not T, and N is A, C, G or T, then the V should hybridize in the mRNA and not within the polyA tail. This serves to anchor the primer at the junction between the end of the mRNA sequence and the beginning of the polyA tail (as shown). The label-tag 4005 may be a series of N's 5′ of the oligo dT region. The primer may optionally include a restriction site 5′ of the label-tag and optionally one or more U bases (shown between the label-tag and the oligo(dT)) that can be subsequently made abasic by UDG. Abasic sites do not serve as efficient template for extension and can thus be used to block or mitigate amplification of the input primer.

The primer is extended to make a copy of the transcript. The extended region is shown by the dashed arrow. Exo I may be used to remove residual oligos that haven't been extended. The products are treated with RNase H and then subjected to poly dA tailing with TdT (step 3001). A second strand is synthesized using a second set of label-tag primers 4009. The second set of primers has from the 5′ end a constant region 4010, a 1^(st) round sequencing primer 4011, a 5′ label-tag 4013, a poly(dT) 4003 stretch and a VN anchor. After the second set of label-tag primers is used to primer second strand synthesis, the sample is treated with Exo I and UDG to remove or disable the residual oligos and the reaction is amplified using PCR using the constant priming regions 4008 and 4009. The label-tags 4013 and 4005 are flanked by sequencing primers 4007 and 4011. The fragments may be separated by size, for example, by gel sizing, and subjected to sequencing using, for example, Illumina paired end sequencing. Efficiency of amplification may be affected by fragment size. Higher primer concentrations, e.g. greater than 3 uM, may be used. A first round sequencing primer (5′ ACACTCTTTCCCTACACGACGCTCTTCCGATCT-3′ SEQ ID NO:1978) and a second round sequencing primer (5′ CGGTCTCGGCATTCCTGCTGAACCGCTCTTCCGATCT-3′ SEQ ID NO. 1979) may be used in subsequent steps to perform primer extension based sequencing using standard methods, for example, next generation sequencing methods commercialized by Illumina, Inc., Life Technologies and Roche 454. The sample prep methods for these manufacturers use adaptor ligation and can be modified to include counters within the adaptors that are added during sample prep. Methods for sequencing have been reviewed, for example, in Metzker, Nature Reviews Genetics Vol. 11, pp 31-46 (2010) which is incorporated herein by reference in its entirety. Methods include, for example, use of reversible terminator chemistry, virtual terminators and ligation based methods.

FIG. 27 shows another method for attaching label-tags. As in FIG. 26, polyadenylated RNA 4001 is reverse transcribed using a first primer [UR1_label] that has from the 5′ end, a priming region 4008, a 2^(nd) round sequencing primer 4007, a 3′ label-tag 4005, a region of uracil bases, a poly(dT) region 4003 and a VN at the 3′ end as described above where V is A, C or G but not T, and N is A, C, G or T. The [UR1_label] primer is extended to make a copy of the transcript. Exo I may be used to remove residual oligos that haven't been extended. The products are treated with RNase H and then subjected to poly dG tailing with TdT. A second strand is synthesized using a second set of label-tag primers [UF1_label]. The second set of primers has from the 5′ end a constant region 4009, a 1^(st) round sequencing primer 4011, a 5′ label-tag 4013, a poly(dC) 4015 stretch and a DN anchor where D is any base but C. After the second set of label-tag primers is used to primer second strand synthesis, the sample is treated with Exo I and UDG to remove or disable the residual oligos and the reaction is amplified using PCR using the constant priming regions 4008 and 4009. The label-tags 4013 and 4005 are flanked by sequencing primers 4007 and 4011. The fragments may be separated by size, for example, by gel sizing, and subjected to sequencing using, for example, Illumina paired end sequencing. Unlike the method shown in FIG. 26 the use of polyG tailing after 1^(st) strand synthesis reduces the self complementarity between the ends of the strands. Instead of polyA and polyT which are complementary the strands have polyG and polyT or polyC and poly A.

In another aspect shown in FIG. 28A the primer may have the following sequence in the following order (5′ to 3′): oligo dT, a first sequence, a restriction site, a label-tag sequence, a second sequence that is complementary to the first sequence, another dT region, 1-4 U's, V and N. Such a sequence is shown in FIG. 28A (SEQ ID No. 1977). The first and second complementary sequences for the step of a hair pin and the label-tag and the restriction site (Not I in the example shown), form the loop. The formation of the stem-loop structure allows for a shorter length of oligo dT between the label-tag and the target mRNA.

The primer is hybridized to the mRNA and extended using the hybridized mRNA as template. The mRNA can then be digested and the cDNA resulting from the extension of the primer is tailed at the 3′ end, for example, by the addition of a run of poly (dA) using polyA polymerase (PAP) or tailing using TdT. Primers that have not been extended can be digested with a 3′ to 5′ single stranded exonuclease like Exo I. A second strand cDNA can be synthesized by extending a primer complementary to the added 3′ tail, for example polyT. The now double stranded products can be randomly fragmented with DNase, and digested with the restriction enzyme (e.g. Not I). This is shown schematically in FIG. 28B. Adaptors can be ligated to the fragments and the fragments can be amplified. The adaptors may contain priming sites for sequencing. The ligation of an adaptor at the Not I cleavage site positions a sequencing primer near the label-tag and facilitates sequencing of the label. Prior to the PCR amplification step the sample can be treated with UDG to remove excess unincorporated primer with label-tags. The UDG treatment removes the uracils from the label-tag primer extension product so that the strand is not copied 5′ of that region. The oligo dT regions 3203 flank the stem regions 3205 which flank the label-tag 3007 and the restriction site 3009. The target region 3211 is between the region added by tailing 3213 and the second oligo dT region 3203 b. The full length product is amplified by PCR, fragmented with DNAse to generate fragments with blunt ends. Digested with the restriction enzyme to generate a site for adaptor ligation adjacent to the label. Adaptors 3215 are ligated, resulting in a sequencing primer being positioned near the label. The sequencing is performed through the label-tag, the second step region 3205 b, the second oligo dT region 3203 b and into the target 3211.

The oligon dT region, a region containing 1 or more uracil bases, a 3′ label-tag region and a constant region for subsequent analysis. An exemplary primer may be, (SEQ ID NO. 1976) NVTTTTTTTTTTTTTTUUUCANNNNNNNNNNNNgatctagccttctcgccaagtcgtccttacggctctggctaga gcatacggcagaag

Exo I is used to remove the residual oligos and RNase H plus poly dA tailing with TdT is used to add a 3′ poly A tail to the first strand cDNA. A second strand cDNA is synthesized using a primer having a second label-tag, an oligo dT region and a second constant region. Exo 1 and UdG are used to remove residual oligos. In the oligos N is A, C, G or T and V is A, C or G but no T. This facilitates the primer docking at the start of the A homopolymer rather than further down the run of A's. A 72 base single read or paired end read sequencing run can be performed to provide 39 bases of the 3′ mRNA end ahead of the polyA site.

In some aspects the probability that any two targets are labeled with the same label-tag may be decreased by using two or more labeling steps. For example, a first labeling step where each target has a label-tag selected from a set of label-tags followed by a second labeling set using the same set of label-tags. The first labeling event will be independent of the second so the probability that the first and second labeling events will both be the same in two independent targets is the product of the probability of two targets having the same label-tag in either step. If there are N possible label-tags, and the first target is labeled first with label-tag N1 and then with label-tag N4, the probability that a second target will be labeled also with N1 and then N4 is 1/N². So if there are 100 different label-tags, the probability that two targets will be labeled with the same label-tag in the first round and the same label-tag in the second round is 1/10,000.

In another aspect a first round of labeling may be done with 16 probes (for example, all possible 2 base combinations) and then a second round of labeling is done using the same 16 probes. The chance of any one probe attaching to a given target occurrence in the first round is 1 out of 16, the chance that the same probe will attach to the second target is 1/16 and the chance that the same two probes will attach is 1/16× 1/16 or 1/256.

In another aspect reversible terminators are used to add a sequence to the end of each target being counted. For example, a 6 base sequence may be added and the chance of two being the same is 1 in 4⁶ or 1 in 4096. See, for example, WO 93/06121 and U.S. Pat. No. 6,140,493 which disclose stochastic methods for synthesizing random oligomers.

There is a finite set of label-tags, L_(1-x) and each target to be detected is present in the sample at a certain integer occurrence (T1_(1-t) ¹, T2_(1-t) ², . . . TN_(1-t) ^(n)). In a preferred aspect, the method is used to count the number of each of the different targets, (e.g. how many occurrences of T1, how many of T2, . . . how many of TN) in the sample. The targets are independently labeled with the label-tag molecules. Labeling is stochastic, so that any given target occurrence can be labeled with any one of the label-tags. For example, T1-1/L689, T1-2/L3, T1-3/L4,567 and so on. For Target 2, any given occurrence can also be labeled with any of the label-tag molecules. This might generate, for example, (T2-1, L5), (T2-2, L198), (T2-3, L34) and so on. There are multiple copies of each label-tag so T2-1 might be labeled with L5 and T1-500 may also be labeled with L5.

The methods disclosed herein may be used to measure random cell-to-cell variations in gene expression within an isogenic population of cells. Such variation can lead to transitions between alternative states for individual cells. For example, cell-to-cell variation in the expression of comK in B. subtilis has been shown to select cells for transition to the competent state in which genes encoding for DNA uptake proteins are expressed. See, Maamar et al. Science 317:526-529 (2007) which is incorporated herein by reference.

The methods disclosed herein may be used to count the number of transcripts or DNA targets of a single type in a single cell (or small group of cells) and to separately count many different transcript types from a single cell (or small group of cells). The transcriptome or genome from a single cell or a few cells can thus be compared to the transcriptome or genome from another cell or group of cells. This comparison may be between different cell types, the same cell type at different developmental stages or under different environmental circumstances or between different portions of a tissue that is a mosaic.

Stochastic fluctuations in the levels of cellular components may play an essential role in cellular activities and may facilitate probabilistic differentiation strategies. For a review see Eldar and Elowitz, Nature 467, 167-173 (2010), which is incorporated herein by reference. Pooling of the nucleic acids from a larger number of cells may mask differences between individual cells or clusters of cells. Single cell analysis methods have been reported previously. See, for example, Aumann et al., (2008) Exp. Neurol. 213:419-430, Cauli et al., (1997) J. Neurosci. 17:3894-3906, Neuhoff et al. (2002) J. Neurosci. 22:1290-1302, Stahlberg and Bengtsson (2010) PCR Methods 50:282-288 and Esumi et al. Neurosci Res. 2008, 6(4):439-51, Other methods for analysis or the transcriptome of single cells that do not provide unique label-tags are impacted by amplification bias, for example, Tang et al. (Nature Protocols 5, 516-535 (2010) uses deep sequencing after 29 cycles of PCR to analyze the transcriptome of single mouse oocytes. Targets that did not amplify efficiently in the initial rounds of amplification may go undetected by sequencing.

Methods for analyzing gene expression at the single cell level is difficult because of the relatively small amount of mRNA available, sometimes being less than about 1 pg. Standard methods of mixing microliter volumes such as shaking, triturating or vortexing can fail to product sufficient turbulence at small scales so other methods of mixing may be desirable. Acoustic microstreaming uses sound waves in the audible spectrum to rapidly and effectively mix solutions in volumes of about 10 to about 100 ul (see Petkovic-Duran et al. (2009) BioTechniques 47:827-834 and US Patent 20090034360). Methods for improving the yield of cDNA from reverse transcription of small amounts of RNA, such as those amounts that might be obtained from a single cell have been developed and may be used in conjunction with the reverse transcription methods for associating unique identifiers with individual molecules that are disclosed herein. In one aspect methods for improved mixing of the reverse transcription reaction may be used. One such method, acoustic microstreaming, is described in Boon et al., BioTechniques 50(2), 116-119. Acoustic microstreaming is a phenomenon where sound waves propagating around a small obstacle create a mean flow near the obstacle. Boon et al. describe using acoustic microstreaming at audio frequencies by ensuring the system has a liquid-air interface with a small radius of curvature that causes the entire drop to oscillate. This method was most effective at RNA concentrations of 0.1 to 1 pg/ul).

In one aspect, polyadenylated RNA from a single cell is analyzed by the methods disclosed herein. After cell lysis the poly A RNA may be enriched by capture on a solid support, such as a bead, having oligo dT attached or the amplification can be performed on the lysate. A labeled-cDNA copy of the RNA is made by hybridizing a primer that has an oligo dT region and a label-tag region. The label-tag region being 5′ of the oligo dT region. Preferably there is an amplification sequence that is 5′ of the label-tag region so that the label-tag region, which is variable between primers, is between a 5′ common amplification primer sequence and a 3′ oligo dT region. Second strand cDNA is then synthesized using standard methods, for example use of RNaseH and DNA polymerase. The resulting dsDNA can then be linearly amplified depending on the amplification primer sequence. For example, if the amplification primer sequence is a T7 RNA polymerase promoter sequence, antisense RNA can be generated by IVT using T7 RNA pol. If the amplification prime sequence includes a site for s nicking enzyme (e.g. Nt. BspQ1), nicking enzyme strand displacement can be used to generate DNA copies of the RNA targets. The copies can then be modified to include sequencing primers at one or both ends and the products can be sequenced. Sequence information is collected for the tag and enough of the adjacent sequence to provide an identification of the target.

The examples provided herein demonstrate the concept of using a stochastic labeling strategy in the high sensitivity detection and counting of individual DNA molecules. The difficult task of quantifying single nucleic acid molecules is converted into a simple qualitative assay that leverages the statistics of random probability; and at the same time, the requirement of single molecule detection sensitivity is achieved with PCR for the robust amplification of single DNA molecules. In some aspects improved methods for amplification will be used. For example, linear amplification methods may be used to mitigate the representation distortions created by exponential cycling in PCR. Given the lack of available techniques for single molecule counting, and the increasing need for its use, the new concept of stochastic labeling is likely to find numerous applications in the near future.

The examples of the present invention presented below are provided only for illustrative purposes and not to limit the scope of the invention.

EXAMPLES

To demonstrate stochastic labeling, an experiment was performed to count small numbers of nucleic acid molecules in solution. Genomic DNA from a male individual with Trisomy 21 was used to determine the absolute and relative number of DNA copies of chromosomes X, 4 and 21, representing 1, 2 and 3 target copies of each chromosome, respectively. Genomic DNA isolated from cultured B-Lymphocytes of a male Caucasian with Trisomy 21 was purchased from The Coriell Institute for Medical Research (Catalog #GM01921). The DNA quantity was determined by PICOGREEN dye (Invitrogen) measurements using the lambda phage DNA provided in the kit as reference standard. DNA quality was assessed by agarose gel electrophoresis.

The DNA concentration in the stock solution was measured by quantitative staining with picogreen fluorescent dye, and dilutions containing 3.62 ng, 1.45 ng, 0.36 ng and 0.036 ng were prepared. In each dilution, the number of copies of target molecules in the sample was calculated from a total DNA mass of 3.5 pg per haploid nucleus (see, T. R. Gregory et al., Nucleic Acids Res 35, D332 (2007), and represent approximately 500, 200, 50 and 5 haploid genomes. The absolute quantity of DNA in the sample was determined by optical density measurements and quantitative staining with PICOGREEN fluorescent dye (Invitrogen) prior to making dilutions.

As outlined in FIG. 3, the genomic DNA sample 301 was first digested to completion with the BamHI restriction endonuclease to produce 360,679 DNA fragments 305. A diverse set of label-tags consisting of 960 14-nucleotide sequences was synthesized as adaptors harboring BamHI overhangs (SEQ ID Nos. 44-1963). Genomic DNA was digested to completion with BamHI (New England BioLabs, NEB) and ligated to a pool of adaptors consisting of an equal concentration of 960 distinct label-tags (as shown in FIG. 3). Each adaptor consists of a universal PCR priming site, a 14 nucleotide long counter sequence and a BamHI overhang (similar to the form of the adaptor shown in FIG. 4. The sequence of the label-tag adaptors SEQ ID Nos. 44-1963 were selected from an all-possible 4¹⁴ nucleotide combination to be of similar melting temperature, minimal self-complementation, and maximal differences between one-another. Homopolymer runs and the sequence of the BamHI restriction site were avoided. Each pair, for example, SEQ ID Nos. 44 and 45, form an adaptor pair that has a region of complementarity starting at base 12 in SEQ ID No. 44 and base 5 in SEQ ID No. 45:

SEQ ID 44 5'CGACAGACGCCTGATCTTTTGTTAGCCGGAGT 3' SEQ ID 45 3'ACTAGAAAACAATCGGCCTCACTAG5'

The adaptors have a 5′ overhang of 11 bases in the even numbered SEQ IDs and 4 bases (GATC) in the odd numbered SEQ IDs. Oligonucleotides were synthesized (Integrated DNA Technologies) and annealed to form double-stranded adaptors prior to pooling. For ligation, the digested DNA was diluted to the desired quantity and added to 100 pmoles (equivalent to 6×10¹³ molecules) of pooled label-adaptors, and 2×10⁶ units (equivalent to 1×10¹³ molecules) of T4 DNA ligase (NEB) in a 30 μl reaction. The reaction was incubated at 20° C. for 3 hours until inactivation at 65° C. for 20 minutes.

In some aspects of the stochastic labeling reaction, each DNA fragment-end randomly attaches to a single label-tag by means of enzymatic ligation of compatible cohesive DNA ends to generate labeled fragments. High coupling efficiency is achieved through incubation with a large molar excess of label-tags and DNA ligase enzyme (˜10¹³ molecules each). At this stage, the labeling process is complete, and the samples can be amplified as desired for detection. A universal primer may be added either by including as part of the adaptor or by extension of a primer containing the universal priming region in a subsequent step, and the entire population of labeled DNA fragments may be PCR amplified. The PCR reaction preferentially amplifies approximately fragments in the 150 bp-2 kb size range. Larger fragments, greater than about 9000 bases, for example, do not amplify efficiently under the selected PCR conditions. There are approximately 80,000 such fragments when the human genome is fragmented with BamHI. (FIG. 19). Adaptor-ligated fragments were amplified in a 50 μl reaction containing 1× TITANIUM Taq PCR buffer (Clontech), 1M betaine (Sigma-Aldrich), 0.3 mM dNTPs, 4 μM PCR004StuA primer (SEQ ID No. 1974), 2.5U Taq DNA Polymerase (USB), and 1× TITANIUM Taq DNA polymerase (Clontech). An initial PCR extension was performed with 5 minutes at 72° C.; 3 minutes at 94° C.; followed by 5 cycles of 94° C. for 30 seconds, 45° C. for 45 seconds and 68° C. for 15 seconds. This was followed by 25 cycles of 94° C. for 30 seconds, 60° C. for 45 seconds and 68° C. for 15 seconds and a final extension step of 7 minutes at 68° C. PCR products were assessed with agarose gel electrophoresis and purified using the QIAQUICK PCR purification kit (Qiagen).

The purified PCR product was denatured at 95° C. for 3 minutes prior to phosphorylation with T4 polynucleotide kinase (NEB). The phosphorylated DNA was ethanol precipitated and circularized using the CIRCLIGASE II ssDNA Ligase Kit (Epicentre). Circularization was performed at 60° C. for 2 hours followed by 80° C. inactivation for 10 minutes in a 40 μl reaction consisting of 1× CIRCLIGASE II reaction buffer, 2.5 mM MnCl₂, 1M betaine, and 200 U CIRCLIGASE II ssDNA ligase. Uncirculated DNAs were removed by treatment with 20 U Exonuclease I (Epicentre) at 37° C. for 30 minutes. Remaining DNA was purified with ethanol precipitation and quantified with OD₂₆₀ measurement.

Amplification of gene targets. Three assay regions were tested: One on each of chromosomes 4, 21 and X. The genomic location (fragment starting and ending positions are provided), of the selected fragments are as follows: Chr4 106415806_106416680 (SEQ ID No. 1), Chr21 38298439_38299372 (SEQ ID No. 2), and ChrX 133694723_133695365 (SEQ ID No. 3). The lengths are 875, 934 and 643 bases respectively. The circularized DNA was amplified with gene specific primers (SEQ ID Nos. 4-9) in a multiplex inverse PCR reaction. PCR primers were picked using Primer3 (available from the FRODO web site hosted by MIT) to yield amplicons ranging between 121 and 168 bp. PCR was carried out with 1× TITANIUM Taq PCR buffer (Clontech), 0.3 mM dNTPs, 0.4 μM each primer, 1× TITANIUM Taq DNA Polymerase (Clontech), and ˜200 ng of the circularized DNA. After denaturation at 94° C. for 2 minutes, reactions were cycled 30 times as follows: 94° C. for 20 seconds, 60° C. for 20 seconds, and 68° C. for 20 seconds, with a 68° C. final hold for 4 minutes. PCR products were assessed on a 4-20% gradient polyacrylamide gel (Invitrogen) and precipitated with ethanol.

The amplified DNA was fragmented with DNase I, end-labeled with Biotin, and hybridized to a whole-genome tiling array which spans the entire non-repetitive portion of the genome with uniform coverage at an average probe spacing of ˜200 nt (see Matsuzaki et al., Genome Biol 10, R125 (2009) and Wagner et al. Systematic Biology 43, 250 (1994)). In FIG. 19, probe intensity (“Array Intensity”) from a whole-genome tiling array (y-axis) is grouped into 200 nt bins by the length of the BamHI fragment on which it resides. The sizes and sequences of restriction fragments from a selected genome can be predicted and binned according to size. High probe intensity demonstrates the preferential amplification of fragments in the 600 bp˜1.2 kb size range (x-axis, log-scale). The computed size distribution of BamHI restricted fragments in the reference genome sequence (NCBI Build 36) is shown by the curve labeled “Number of Fragments”. After circularization of the amplified products to obtain circles as shown in FIG. 3, three test target fragments were isolated using gene-specific PCR; one on each of chromosomes X, 4, and 21, and prepared for detection.

The three labeled targets were counted using two sampling techniques: DNA microarrays and next-generation sequencing. For the array counting, a custom DNA array detector capable of distinguishing the set of label-tags bound to the targets was constructed by dedicating one array element for each of the 960 target-label-tag combinations. Each array element consists of a complementary target sequence adjacent to one of the complements of the 960 label-tag sequences (as shown in FIG. 2C).

Array Design: For each gene target assayed, the array probes tiled consist of all possible combinations of the 960 counter sequences connected to the two BamHI genomic fragment ends (FIG. 5). An additional 192 counter sequences that were not included in the adaptor pool were also tiled to serve as non-specific controls. This tiling strategy enables counter detection separately at each paired end, since each target fragment is ligated to two independent counters (one on either end).

Arrays were synthesized following standard Affymetrix GENECHIP manufacturing methods utilizing lithography and phosphoramidite nucleoside monomers bearing photolabile 5′-protecting groups. Array probes were synthesized with 5′ phosphate ends to allow for ligation. Fused-silica wafer substrates were prepared by standard methods with trialkoxy aminosilane as previously described in Fodor et al., Science 251:767 (1991). After the final lithographic exposure step, the wafer was de-protected in an ethanolic amine solution for a total of 8 hrs prior to dicing and packaging.

Hybridization to Arrays: PCR products were digested with Stu I (NEB), and treated with Lambda exonuclease (USB). 5 μg of the digested DNA was hybridized to a GeneChip array in 112.5 μl of hybridization solution containing 80 μg denatured Herring sperm DNA (Promega), 25% formamide, 2.5 pM biotin-labeled gridding oligo, and 70 μl hybridization buffer (4.8M TMACl, 15 mM Tris pH 8, and 0.015% Triton X-100). Hybridizations were carried out in ovens for 16 hours at 50° C. with rotation at 30 rpm. Following hybridization, arrays were washed in 0.2×SSPE containing 0.005% Trition X-100 for 30 minutes at 37° C., and with TE (10 mM Tris, 1 mM EDTA, pH 8) for 15 minutes at 37° C. A short biotin-labeled oligonucleotide (see 519 in FIG. 5) was annealed to the hybridized DNAs, and ligated to the array probes with E. coli DNA ligase (USB). Excess unligated oligonucleotides were removed with TE wash for 10 minutes at 50° C. The arrays were stained with Streptavidin, R-phycoerythrin conjugate (Invitrogen) and scanned on the GCS3000 instrument (Affymetrix).

In order to maximize the specificity of target-label-tag hybridization and scoring, a ligation labeling procedure was employed on the captured sequences (FIG. 5). Thresholds were set to best separate the intensity data from the array into two clusters, one of low intensity and one of high intensity to classify label-tags as either being used or not (FIGS. 20, 21 and 25). A label-tag was scored as “present” and counted if its signal intensity exceeded the threshold. To count label-tags thresholds for the array intensity, or the number of sequencing reads were set. Appropriate thresholds were straightforward to determine when used and un-used label-tags fall into two distinct clusters separated by a significant gap. In situations where a gap was not obvious, the function normalmixEM in the R package mixtools was used to classify label-tags. This function uses the Expectation Maximization (EM) algorithm to fit the data by mixtures of two normal distributions iteratively. The two normal distributions correspond to the two clusters to be identified. The cluster of label-tags with a high value is counted as “used”, and the other as “not used”. The average of the minimum and maximum of the two clusters, (I_(min)+I_(max))/2, was applied as the threshold for separating the two clusters.

Sampling error calculation. A sampling error can be introduced when preparing dilutions of the stock DNA solution. This error is a direct consequence of random fluctuations in the number of molecules in the volume of solution sampled. For example, when exactly 10 μl of a 100 μl solution containing 100 molecules is measured, the actual number of molecules in the sampled aliquot may not be exactly 10. The lower the concentration of the molecules in the entire solution, the higher the sampling error, and the more likely the actual abundance in the sampled aliquot will deviate from the expected abundance (n=10). To calculate sampling errors, the number of molecules for each chromosome target in the stock DNA solution was determined and numerical simulations were performed to follow the dilution steps in preparing the test samples (3.62 ng, 1.45 ng, 0.36 ng and 0.036 ng). To illustrate, if the dilution step is sampling 1 μl of a 25 μl solution containing 250 molecules, 25 bins are created and each of the 250 molecules is randomly assigned into one of the bins. A bin was chosen at random and the number of molecules assigned to that bin was counted to simulate the process of sampling 1/25^(th) of the entire solution. If a serial dilution was performed, the simulation process could be repeated accordingly. For each dilution, the observed copy number ratios of Chr 4:X or 21:X for 10,000 independent trials are summarized as observed medians, along with the 10^(th) and 90^(th) percentiles and shown in FIGS. 12 and 13.

As an alternate form of detection, the labeled samples can be sequenced using second-generation sequencing methods. This was demonstrated by submitting samples to two independent DNA sequencing runs using SOLID sequencing (ABI). The arrangement and position of the adaptors and PCR primers used to convert the DNA sample hybridized to microarrays into sequencing templates are shown schematically in FIG. 10. For additional detail and exemplary sequences see also, FIG. S5 of Fu et al. PNAS, vol. 108(22):9026-9031 (2011), which is incorporated herein in its entirety by reference. The circularized junction 515 is located between the two counter label-tags. PCR primers (3116-3118) that have restriction sites are used to amplify two fragments. Exemplary PCR primers are as follows “Fsac” 3116, “PCR004StuA_Bgl, 3117 and “Rsac” 3118. The PCR amplification introduces restriction sites at the ends of the fragments. The fragments are digested with the restriction enzymes to generate ends compatible with ligation to sequencing adaptors “P2 Sac 1 adaptor” and “P1 Bgl II adaptor” which also may include an encoder sequence to identify different samples. In the example the digestion is with Bgl II and Sac I because those are the sites that were included in the primers 3116-3118, but a variety of restriction enzymes could be used. The sequencing adaptors, including the priming sites for the sequencing reaction, are ligated to the ends to generate fragments that have a label-tag sequence and a portion of the target that is about 48 to 94 base pairs in length flanked by sequences for use with SOLID sequencing. In one embodiment the sequence of the entire label-tag is determined, for example 14 bases, and enough of the target to determine identity of the target. Read lengths may be, for example, 35 to 50 bases. The number of bases of sequence needed to unambiguously assign an identity to each read of a fragment will vary depending on the number of possible targets and the difference between targets. Reads of 6 to 21 bases of the target were used in the present examples. If fragments are very similar, for example, different alleles of a variant, such as a SNP or indel, it may be necessary to sequence the variable region or a portion of the variable region.

Validation by DNA sequencing (First SOLID run). DNA targets that were used for hybridization to arrays were converted to libraries for sequencing on the SOLID instrument (ABI). P1 and P2 SOLID amplification primers were added to the DNA ends through adaptor ligation and strand extension from gene-specific primers flanked by P1 or P2 sequences (FIG. 10). Each sample received a unique ligation adaptor harboring a 4-base encoder (SEQ ID Nos. 34-43) that unambiguously identifies the originating sample of any resulting read. Each adaptor includes two strands, SEQ ID Nos. 34 and 35, 36 and 37, 38 and 39, 40 and 41 or 42 and 43, that hybridize to form a double stranded region of 29 base pairs and a single stranded 4 base overhang (GATC). Individual libraries were prepared for each sample, and quantified with picogreen before equal amounts of each sample was combined into a single pooled library. DNA sequencing was performed on SOLID v3 by Cofactor Genomics. A total of ˜46 million 50 base reads were generated. Each read is composed of three segments, corresponding to the sample encoder, label-tag sequence and gene fragment (FIG. 10). Reads were removed if: uncalled color bases were present, the average Quality Value (aQV) of the whole read <10, the aQV of the sample encoder <20, or the aQV of the label-tag sequence <18.40% of the raw reads were removed. Filtered reads were mapped to reference sequences using the program Short Oligonucleotide Color Space (SOCS), available from ABI with a maximum tolerance of 4 color mismatches between the first 45 color bases in each read and reference sequences (the last 5 color bases on 3′ end of each read were trimmed in alignment). About 64.3% reads were uniquely mapped to reference sequences, of which 89.5% (16 million) have high mapping quality, i.e., with no mismatch in the sample encoder and at most 1 mismatch in the label-tag sequence. These high-quality reads, accounting for ˜35% of the total reads generated, were used in subsequent counting analysis.

Sequencing replication (Second SOLID run). An aliquot of the exact same DNA library originally sequenced by Cofactor Genomics was subsequently re-sequenced by Beckman Coulter Genomics. Approximately 50 million 35 base reads were generated, and processed following the same rules. Approximately 61% of the raw reads passed quality filters, of which 81% uniquely mapped to a reference sequence with a maximum tolerance of 3 color mismatches (An adjusted mismatch tolerance was applied in the alignment step to account for the shorter length of these reads). Of the mapped reads, 91% (22.5 million) are of high mapping quality, i.e., with perfect match in the sample encoder and at most 1 mismatch in the label-tag sequence. These high-quality reads (45% of the total raw reads generated) were used for counting analysis.

Between several hundred thousand to several million reads were used to score the captured label-tags. Table 1 shows the number of mapped reads from SOLID DNA sequencing.

TABLE 1 DNA sample 5 ng 2 ng 0.5 ng 0.05 ng 0 ng Chr4 Left side 1^(st) SOLiD run 709,076 252,211 237,380 316,629 1,204 2^(nd) SOLiD run 621,372 73,962 189,937 237,520 411 Right side 1^(st) SOLiD run 1,724,955 1,662,958 1,114,246 2,201,078 3,353 2^(nd) SOLiD run 1,422,673 1,359,512 839,775 980,616 2,386 Chr21 Left side 1^(st) SOLiD run 1,615,416 1,474,208 832,234 1,428,540 1,851 2^(nd) SOLiD run 1,296,685 1,038,456 622,429 930,461 840 Right side 1^(st) SOLiD run 1,124,772 886,421 551,192 849,204 821 2^(nd) SOLiD run 910,298 522,358 367,207 479,621 224 ChrX Left side 1^(st) SOLiD run 444,960 316,975 254,386 515,213 744 2^(nd) SOLiD run 266,606 157,860 137,706 220,121 5 Right side 1^(st) SOLiD run 1,227,047 921,214 777,033 1,064,531 64 2^(nd) SOLiD run 1,043,475 768,296 559,038 695,873 43

Thresholds were set for the number of sequencing reads observed for each label-tag, and score a label-tag as “present” and counted if the number of sequencing reads exceeded the threshold. Label-tag usage summaries from experimental observations or from the stochastic modeling are shown in Table 2. The number of attached label-tags, k, detected for each target in each dilution either by microarray counting or sequence counting is presented in Table 2, and plotted in FIG. 12.

Several dilutions (3.62 ng, 1.45 ng, 0.36 ng and 0.036 ng) of DNA isolated from cultured lymphoblasts of a Trisomy 21 male individual were processed for microarray hybridization (FIG. 12 left) and DNA sequencing (FIG. 12 right). Three gene targets were tested from chromosome X, 4 and 21, and observed numbers of detected label-tags are shown (lines 1201). The number of target molecules for each sample was determined from the amount of DNA used, assuming a single haploid nucleus corresponds to 3.5 pg. For comparison, the calculated number of label-tags expected to appear using a stochastic model are also plotted, lines 1202. Numerical values are provided in Table 4. Relative copy ratios of the three gene targets (FIG. 13): ChrX (right bar), Chr4 (left bar) and Chr21 (center bar) representing one, two and three copies per cell, respectively. The calculated number of target molecules was determined from the number of label-tags detected on microarrays (Table 4, column 9) or from the SOLiD sequencing data. For each sample dilution, the copy number ratio of each gene target relative to ChrX is shown for the microarray (FIG. 13 left) and for SOLiD sequencing (FIG. 13 right). For comparison, FIG. 13 also shows relative copy ratios obtained from in silico sampling simulations, where circles indicate the median values from 10,000 independent trials and error bars indicate the 10^(th) and 90^(th) percentiles. The 90^(th) percentile values of the relative copy ratios at the lowest concentration (0.036 ng) are provided (4.5 and 6.67).

TABLE 2 3.62 1.45 0.36 0.036 DNA sample ng ng ng ng 0 ng Chr4 Stochastic Model 633 336 98 10 0 Left side Microarray 501 260 102 14 0 1^(st) SOLiD run 513 251 101 14 0 2^(nd) SOLiD run 516 273 102 14 0 Right Array 525 256 107 14 0 side 1^(st) SOLiD run 544 291 103 13 1 2^(nd) SOLiD run 557 307 103 13 1 Chr21 Stochastic Model 769 457 143 15 0 Left side Microarray 651 335 160 20 0 1^(st) SOLiD run 678 381 152 20 0 2^(nd) SOLiD run 665 358 161 18 0 Right Microarray 627 341 157 20 0 side 1^(st) SOLiD run 650 381 146 19 0 2^(nd) SOLiD run 653 379 146 19 0 ChrX Stochastic Model 400 186 50 5 0 Left side Microarray 281 148 50 11 0 1^(st) SOLiD run 290 149 43 11 0 2^(nd) SOLiD run 300 150 45 11 0 Right Microarray 306 133 48 10 1 side 1^(st) SOLiD run 336 153 50 12 0 2^(nd) SOLiD run 344 167 43 11 0

The counting results span a range of approximately 1,500 to 5 molecules, and it is useful to consider the results in two counting regimes, below and above 200 molecules. There is a striking agreement between the experimentally observed number of molecules and that expected from dilution in the first regime where the ratio of molecules to label-tags (n/m)<0.2 (Table 2). Below 200 molecules the data are in tight agreement, including the data from the lowest number of molecules, 5, 10 and 15 where the counting results are all within the expected sampling error for the experiment (The sampling error for 10 molecules is estimated to be 10±6.4, where 10 and 6.4 are the mean and two standard deviations from 10,000 independent simulation trials).

In the second regime above 200 molecules, there is an approximate 10-25% undercounting of molecules, increasing as the number of molecules increases. This deviation may be due to a distortion in the amplification reaction. PCR-introduced distortion occurs from small amounts of any complex template due to the differences in amplification efficiency between individual templates (2, 3). In the present case, stochastic labeling will produce only one (at low n/m ratios), and increasingly several copies (at higher n/m ratios) of each template. Modeling suggests that simple random dropout of sequences (PCR efficiencies under 100%) generate significant distortion in the final numbers of each molecule after amplification. At any labeling ratio, random dropout of sequences due to PCR efficiency will result in an undercount of the original number of molecules. At high n/m ratios, the number of label-tags residing on multiple targets will increase and have a statistical survival advantage through the PCR reaction causing greater distortion. In support of this argument, a wide range of intensities on the microarray and a wide range in the number of occurrences of specific sequences in the sequencing experiments were observed (FIGS. 20 and 25). For additional plots of label-tags observed in the microarray experiments and by sequencing see FIGS. S4A and S4B of Fu et al. PNAS, vol. 108(22):9026-9031 (2011). This effect can be reduced by carrying out the reaction at n/m ratios near or less than 0.2, increasing the number of label-tags m, further optimization of the amplification reaction, or by employing a linear amplification method. Other factors, such as errors from inaccurate pipetting, could also contribute.

The lymphoblast cell line used in this study provides an internal control for the relative measurement of copy number for genes residing on chromosomes X, 4 and 21. FIG. 13 presents the relative number of molecules from all three chromosomes normalized to copy number 1 for the X chromosome. As shown, the measurements above 50 molecules all yield highly precise relative copy number values. At low numbers of molecules (0.036 ng), uncertainty results because the stochastic variation of molecules captured by sampling an aliquot for dilution are significant. Numerical simulations were performed to estimate the sampling variation, and summarized medians, along with the 10^(th) and 90^(th) percentiles of the copy number ratios and are shown in FIG. 13 as circles and range bars, respectively. At the most extreme dilutions, where ˜5, 10, and 15 molecules are expected for the chromosome X, 4 and 21 genes, the copy number ratios fall within the expected sampling error.

Overall, the identity of label-tags detected on the microarrays and in sequencing are in good agreement, with only a small subset of label-tags unique to each process (Table 7). Despite a high sequencing sampling depth (Table 1), a small number of label-tags with high microarray intensity appear to be missing or under-represented in the sequencing results. In contrast, label-tags that appear in high numbers in the sequencing reaction always correlate with high microarray intensities. No trivial explanation could be found for the label-tags that are missing from any given sequencing experiment. While under-represented in some experiments, the same label-tags appear as present with high sequence counts in other experiments, suggesting that the sequences are compatible with the sequencing reactions.

PCR was used as an independent method to investigate isolated cases of disagreement, and demonstrated that the label-tags were present in the samples used for the sequencing runs. PCR was used to detect the presence of 16 label-tag sequences (Table 3) which were either observed as high or low hybridization intensity on microarrays, and observed with either high or low numbers of mapped reads in SOLID sequencing. The Chr4 gene target was PCR amplified with 3 dilutions (0.1 pg, 1 pg, and 10 pg) of the 3.62 ng NA01921 sample, using the DNA target that was hybridized to microarrays, or the prepared SOLID library template. PCR products were resolved on 4% agarose gels and fluorescent DNA bands were detected after ethidium bromide staining

TABLE 3 1st 2nd Microarray SOLiD Label- SOLiD SOLiD Microarray target library tag ID Label-tag Sequence reads reads intensity template template 112 AGATCTTGTGTCCG     0     2 15,907  1  2 182 ATCTTCGACACTGG     0     1 10,304  3  4 779 TCGAGATGGTGTTC     0     4  9,411  5  6 782 TCGGATAGAGAGCA     0     0  6,716  7  8 783 TCGGTACCAACAAC     1     4 13,132  9 10 290 CCAAGGTTTGGTGA     1    17 10,777 11 12 780 TCGCAAGAGGTAAG     1     1  8,915 13 14 570 GGAGTTACGGCTTT     1     2  8,252 15 16 741 TCAACCAGTAAGCC   794   400    466  17*  18* 424 CTGTAAACAACGCC 1,191 1,292    527  19*  20* 242 CACGATAGTTTGCC   905   781  1,103  21* 22 859 TGTACTAACACGCC   920   892  1,107  23*  24*  83 ACGCTAACTCCTTG 8,629 7,704 19,500 25 26 383 CGTTTACGATGTGG 7,278 6,402 19,022 27 28 804 TCTTAGGAAACGCC     0     0     70  29*  30* 834 TGCAATAGACGACC     0     1     72  31*  32*

Table 3. PCR detection for the presence of label-tag sequences in the processed DNA sample that was hybridized to microarray, or in the DNA sequencing library. Each PCR contained 0.1 pg of template, which represents approximately 1×10⁶ DNA molecules. The number of mapped sequencing reads and the microarray intensity of each of the 16 label-tags for this selected gene target (Chr4, 3.62 ng) are listed. The last 2 columns show the gel lane number containing the indicated sample. Those numbers indicated by an * correspond to reactions where PCR failed to detect the label-tag sequence in the sample.

Although their presence in the sequencing libraries is confirmed, it is unclear why these label-tags are missing or under-represented in the final sequencing data.

To test the stochastic behavior of label-tag selection, the results of multiple reactions at low target concentrations (0.36 and 0.036 ng), where the probability that a label-tag will be chosen more than once is small, were pooled. FIG. 14 shows that the number of times each label-tag is used closely follows modeling for 1,064 data points obtained from microarray counting. The graph is a comparison between experimentally observed label-tag usage rates (microarray results) with those predicted from stochastic model (stochastic model). At low target molecule numbers, the chance of multiple target ligations to the same label-tag sequence is low. It is therefore reasonable to consider data from experiments with low target numbers (0.036 ng and 0.36 ng of DNA), from those experiments, a total of 1,064 label-tags were observed, with the total frequency of label-tag usage ranging from 0 to 6. The theoretically expected label-tag usage frequency for 1,064 target molecules was obtained by performing 5000 simulation runs, with multiple independent reactions simulated in each run. The error bars indicate one standard deviation from the corresponding means.

Furthermore, since each end of a target sequence chooses a label-tag independently, the likely hood of the same label-tag occurring on both ends of a target at high copy numbers can be compared. Table 4 columns 10-11 present the experimentally observed frequency of label-tags occurring in common across both ends of a target and their expected frequency from numerical simulations. No evidence of non-stochastic behavior was observed in this data.

TABLE 4 Expected # Expected # of of label- Microarray Estimated # of Expected # molecules tags in observed # Genomic # of label- of label-tags Microarray inferred from common of label-tags DNA molecules tags at in common observed # microarray across in common Gene amount at either either across of label-tags observed # paired- across target (ng) end end paired-ends L R Avg of label-tags ends paired-ends Chr4 3.62 1034 633 417.68 ± 11.35  501 525 513 733 273.96 ± 10.24  303 1.45 414 336 117.92 ± 7.83  260 256 258 300 69.22 ± 6.43  63 0.36 103 98 9.93 ± 2.81 102 107 104 110 11.26 ± 2.99  20 0.036 10 10 0.11 ± 0.32 14 14 14 14 0.20 ± 0.44 0 0 0 0 0 0 0 0 0 0 0 Chr21 3.62 1551 769 616.74 ± 11.94  651 627 639 1051 425.28 ± 11.37  453 1.45 620 457 217.36 ± 9.51  335 341 338 416 118.79 ± 7.83  130 0.36 155 143 21.37 ± 3.98  160 157 158 172 25.86 ± 4.38  32 0.036 15 15 0.24 ± 0.48 20 20 20 20 0.40 ± 0.62 0 0 0 0 0 0 0 0 0 0 0 ChrX 3.62 517 400 166.63 ± 8.81  281 306 294 351 90.14 ± 7.08  103 1.45 207 186 36.26 ± 4.98  148 133 140 151 20.34 ± 3.94  23 0.36 51 50 2.58 ± 1.52 50 48 49 50 2.45 ± 1.51 4 0.036 5 5 0.03 ± 0.16 11 10 10 10 0.10 ± 0.31 2 0 0 0 0 0 1 0 0 0 0 1 2 3 4 5 6 7 8 9 10  11 Label-tags detected on microarray experiments are quantified in Table 4. Indicated quantities (col. 2) of genomic DNA derived from a Trisomy 21 male sample were tested on 3 chromosome targets (col. 1). The estimated number of copies of target molecules (or haploid genome equivalents, col. 3), the number of label-tags expected by the stochastic model (col. 4), and the actual number of label-tags detected on microarrays (col. 6-8) are summarized. Because each gene target fragment paired-end consists of random, independent label-tag ligation events at the left (L) and the right (R) termini, the number of identical label-tags expected (col. 5) can be predicted from computer simulations, and compared to the number actually detected (col. 11). Given the number of label-tags detected (col. 8), the corresponding number of copies of target molecules (col. 9) in the stochastic model, and the predicted occurrences of identical label-tags across paired-ends (col. 10) were obtained. The numbers in col. 5 and 10 are the means from 5,000 independent simulation runs along with one standard deviation of the corresponding means, given the number of label-tags at either end (col. 4 and col. 9).

The detailed column information for Table 4 is as follows: column 1: name of tested gene targets; column 2: estimated number of target molecules at either left or right end, this number is determined by PICOGREEN dye measurement (Molecular Probes, Inc.), the DNA concentration is also listed in this column; column 3: number of label-tags expected to be observed/used at either end (predicted by theoretical models), given the estimated number of target molecules in 2nd column; column 4: number of label-tags expected to be observed in common across the paired-ends (predicted by theoretical models), given the estimated number of target molecules in 2nd column; column 5: empirically observed number of label-tags used at the left end of gene target; column 6: empirically observed number of label-tags used at the right end of gene target; column 7: empirically observed number of label-tags used in common across the paired-ends; column 8: number of target molecules predicted by theoretical models, based on the empirically observed number of label-tags used (i.e., number in 7th column); column 9: number of label-tags expected to be observed in common across the paired-ends, given the number of target molecules in 8th column; column 10: empirically observed number of label-tags that were used in common across the paired-ends of the gene target.

An array was designed having 48 target sequences. Each target was paired with one of 3840 label-tags or “counters” for a total of 48×3840 or 184,320 probes. The probes were 30 mers (30 nucleotides in length) and the assay was designed to test whether or not the 30 mer imparts sufficient discrimination. Of the 30 bases, 15 bases are from the label-tags and the other 15 bases are derived from the targets. The probes were assayed to determine if each label-target combination hybridizes specifically. A phage RNA ligase was used to join label-tags with targets. Universal priming sites of 18 bases were included on the 5′ end of the label-tags and the 3′ end of the targets, facilitating PCR amplification of the joined label-targets.

To test the method illustrated in FIG. 7, a 1:1 dilution of each of the 3840 counters was mixed with various dilutions of each of the 48 target oligos to simulate different expression levels under ligation conditions so that the 5′ end of the target oligos can be ligated to the 3′ end of the label-tag oligos. In preferred aspects T4 RNA ligase may be used to join the ends of the single stranded oligos. The 5′ and 3′ ends of the target oligos are phosphorylated and the 5′ and 3′ ends of the label-tag oligos are hydroxylated. After the ligation the products are amplified by PCR using primers to the universal priming sequences. Only those fragments that have both universal priming sequences 703 and 711 will amplify efficiently.

Each of the 48 target sequences may be tiled with each of the 3,840 counters, resulting in a total number of features on array=48×3,840=184,320. This is the number of different possible combinations of target with label. The product of the ligation and amplification reactions is hybridized to the array. For each target, the number of features that light up is determined and can be compared to the known copy number of each target in the input sample.

To test the digital counting methods, also referred to as stochastic labeling a collection of label-tag sequences was provided. Each has a common 5′ universal priming sequence, preferably 15-20 bases in length to facilitate amplification, and a 3′ label-tag sequence, preferably 17-21 bases in length. Each type of primer in the collection has the same universal priming sequence but each type has a label-tag sequence that is different from all of the other types in the collection. In one aspect there are about 4,000 to 5,000 different types of label-tag sequences in the collection to be used. For testing the method, a set of 50 target sequences was synthesized. The target sequences each have a universal priming sequence at the 3′ end (5′GCTAGGGCTAATATC-3′SEQ ID NO: 1968, was used in this experiment). Each of the 50 oligo target sequences that were generated has a different 21 base sequence from the GENFLEX array collection of sequences, for example, 5′ GCCATTTACAAACTAGGTATT′3′ SEQ ID NO: 1970. The collection of label-tag oligos and the collection of target oligos was mixed. Various dilutions of the different targets were used in the mixture of targets to simulate a mixed population present at different levels, for example, different expression or copy number levels. T4 RNA ligase was added to ligate the label-tag oligos to the target oligos. There are 5000 different types of label-tag oligos and 50 different types of target oligos so the majority of the target oligos of the same type will be labeled with a type of label-tag oligo that is different from all of the other target oligos of that type. So target oligo type 1, occurrence 1 will be labeled with a label-tag oligo type A (11A) and target oligo type 1, occurrence 2, will be labeled with a different label-tag oligo, label-tag oligo type B (12B). There is a finite and calculable probability that two or more occurrences of the same target type will be labeled with the same label-tag oligo (11A and 12A), but that probability decreases as the number of different types of label-tag oligos increases relative to the number of occurrences of any given type of target.

The ligated target/label-tag oligos are then amplified using primers to the universal priming sites. Label-tags can be incorporated during amplification. The labeled amplification product is then hybridized to an array. For each different possible combination of target (50) and label-tag (5000) there is a different probe on the array that targets that junction of the target ligated to the label. There will therefore be 50×5000 different probes on the array or 250,000 different probes.

Scanned images of the 48×3840 array were analyzed and compared to expected results. A total of 8 of the 48 targets were ligated to a pool of 3840 label-tags (counters). The assay was as shown in FIG. 3. The conditions were single strand deoxyoligonucleotide ligation using a phage RNA ligase to join the label-tags with targets. Universal priming sites on the targets and label-tags were included to enable PCR amplification of the joined label-targets. The ligation conditions were essentially as described in (Tessier, D. C. et al. (1986) Anal Biochem. 158, 171-178, 50 mM Tris-HCl, pH 8, 10 mM MgCl2; 10 ug/mL BSA, 25% PEG, 1 mM HCC, 20 uM ATP; 5:1 acceptor (label-tags) to donor (the 8 targets) ratio at 25 C overnight. The products were amplified using PCR, purified, biotin labeled with TdT, hybridized to the array, washed, stained, and scanned. The expected 8 blocks show hybridization to the array in the expected patterns.

Different ligation conditions were also tested by ligating either a single target or a pool of 48 targets to the 3,840 counters. The concentrations of the targets used in the experiment were high as in the previous experiment so most counters will be ligated to targets. In ligation 1 a single target was ligated to 3,840 label-tags. In ligation 2, 48 targets at 1:1 copy number were ligated to 3,840 label-tags. Ligation 3 is a negative control for PCR so no DNA was added. PCR with the pair of universal primers was performed using the ligation products as template and the products separated on a gel. As expected a band was observed from ligations 1 and 2, but not 3. The PCR products were labeled and hybridized to the array and the scan images after array hybridization were analyzed. As expected no signal was observed for ligation 3, all of the targets were observed for ligation 2 and the single expected target was observed for ligation 1. The single target lights up in the correct region of the chip, but background signal was also observed in unexpected locations. Increased stringency of hybridization conditions can be used to minimize hybridization to unexpected probes of the array.

In another example, conditions for optimization of hybridization to decrease cross hybridization were tested. The products used were as described above and hybridization was performed with formamide and with or without non-specific competitor (herring sperm DNA). The non-specific signal is significantly decreased in the presence of formamide, with and without non specific competitor. This demonstrates that even though the targets and counters alone have 15 bases of complementarity to probes on the array, the combination of target plus counter and the resulting increase to 30 bases of complementarity to the probes, results in specific hybridization. Within the block of 3,480 probes, there is heterogeneity in the hybridization intensity. Preliminary sequence analysis shows a strong correlation of GC content with high signals. To minimize this array probes may be selected to have similar melting temps for the counters or the target-counter combination may be optimized to obtain similar hybridization stabilities. For example, if two targets are to be analyzed the portions of each target that are to be part of the probe may be selected to have similar TMs.

To test the efficiency of T4 RNA ligase in the ligation of label-tags to targets, DNA ligase from E. coli was tested. This required a slight modification of the sample prep (as depicted in FIG. 17A) by creating an overhang site for duplex ligation. The target in this example has a double stranded target specific portion and a single stranded overhang. The overhang may be, for example, a run of inosine bases, for example 6 to 9, or a string of random bases, for example, N6-16. DNA ligase is used to close the gap and generate a ligated product that includes the target strand and a label/counter from the pool of 3,840 counters. The PCR is carried out in the same manner as above using common primers.

The expected targets were observed, but some non-specific bands were also detected in the amplified DNA, even in the absence of the target. This suggests that the some of the 3,840 label-tags are combining with each other when this method is used. Selection of an optimized pool of label-tags may be used to mitigate such interference.

In another example random primed PCR was tested. Instead of a ligation step, the targets have a 3′ random region, that can be, for example, a degenerate region or an inosine region. The label-tags hybridize to the random region and the random region is used as a primer for extension through the label-tag during the PCR step to append a copy of the label-tag and the universal priming site at the 5′ end of the label-tag oligo to the 3′ end of the target. The extended target has a copy of the label-tag sequence and the universal priming sequence and can be amplified by PCR.

In another example, a purification method for removing excess un-ligated counters was tested. The method is shown schematically in FIG. 18. The counters 101 and the targets 2103 are ligated to form counter-target molecules as shown previously. A support bound probe that is complementary to the universal primer at the end of the target oligonucleotides 2105, is used to separate counter-targets and targets from un-ligated counters. The support 2109 may be, for example, a magnetic bead. A second separation can be used to separate counter-targets from un-ligated targets. The second separation uses a support bound probe complementary to the universal priming sequence at the end of the counters 2107. The single capture reduces background amplification. A double round of capture may also be used.

To test the method illustrated in FIG. 8 several adaptors were synthesized. The test adaptor has PCR002 (SEQ ID No. 1969) as top or sense strand and BamAdaAS (SEQ ID No. 1970) as bottom or antisense strand.

PCR002 5' ATTATGAGCACGACAGACGCCTGATCT (1969) BamAdaAS 3' AATACTCGTGCTGTCTGCGGACTAGACTAG 5'P (1970)

The single stranded region on the right is the BamHI single stranded overhang. The adaptor also has a half Bgl II site. The “full length-label” adaptor has SEQ ID No. 1972 as top or sense strand and SEQ ID No. 1973 as bottom or antisense strand.

Sense 5' ATTATGAGCACGACAGACGCCTGATCTNNNNNNNNNNNNNNT AntiSense 3'AATACTCGTGCTGTCTGCGGACTAGANNNNNNNNNNNNNNACTAG

A 5′ phosphate may be added to one or both strands of the adaptor using, for example, T4 polynucleotide kinase. In some aspects a truncated adaptor, such as the one shown in FIG. 4, may be used. The top or sense strand is SEQ ID No. 1974 and the bottom or antisense strand is SEQ ID No. 1975. SEQ ID NOs. 1974 and 1975 are subsequences of SEQ ID NOs. 1972 and 1973 respectively. The N's in SEQ ID Nos. 1972-1975 indicate a variable sequence in the adaptor that is different for each different label. For example, if there are 1,920 different label-tags to be used then the N₁₄ represents the 1,920 different label-tags. In the examples provided, the full length adaptor is 87 bases while the truncated is 57 bases. It is more economical to use shorter sequences particularly when considering that for each different label-tag 2 oligos must be synthesized (e.g. 1,920 label-tags requires 3,840 different oligos). The separate oligos are preferably annealed together prior to being combined into a pool for ligation to fragments. The primer used for amplification may be, for example, SEQ ID NO. 1969 or the 5′ 17 bases of SEQ ID No. 1974.

In another example, a truncated label-tag adaptor was used (SEQ ID Nos. 1974 and 1975). The adaptor ligated fragments were extended to fill in the ends with polymerase prior to PCR. Hybridization was done in duplicate to either the CNV-type array or HG49 design C. Fragmented DNA and non-fragmented DNA were plotted. The intensity of the DNA that was not fragmented prior to hybridization is less than the intensity of the fragmented DNA. The peak of the intensity for both plots is at a fragment size of about 900 base pairs.

FIG. 12 shows counting results for DNA copy number titrations using microarray hybridization on the left or DNA sequencing on the right. Dilutions (3.62 ng, 1.45 ng, 0.36 ng and 0.036 ng) of a DNA sample isolated from cultured lymphoblasts of a Trisomy 21 male individual were processed for microarray hybridization (left) and DNA sequencing (right). Three chromosome targets were tested and observed numbers of counters (Y-axis) are shown (curve 1201). The number of target molecules for each sample (X-axis) was determined from the amount of DNA used, assuming a single cell corresponds to 10 pg. For comparison, the theoretical counter usage rates from the stochastic model equation are also plotted 1202. Numerical values are provided in Table 4.

BamHI cuts the human genome into an estimated 360,679 fragments with a size distribution of 6 bp to 30,020,000 bp. The median size is 5142 bp and the mean is 8320 bp. There are 79,517 fragments in the size range of 150 bp to 2 kb. For testing it may be desirable to choose fragments that meet selected criteria, for example, within a selected size range, select fragments that have more than 1 probe on the HG49m array, exclude fragments that are in known CNV regions, or exclude fragments having a SNP in the first or last 20-30 bases.

The upper panel of FIG. 23 shows the intensities of 1,152 array probes associated with one gene target on chromosome 4, chr4_01s. The data are from the array with 5 ng DNA, i.e., 1000 copies of the tested gene target. The 1,152 probes shown share the same genomic sequence portion, but have different label-tag sequences. Each black dot represents one label-tag sequence. The left 960 dots (on the left side of the dashed vertical line) correspond to specific label-tags (i.e., label-tags used in ligation reaction), and the 192 dots to the right of the dashed vertical line correspond to non-specific label-tags (i.e., label-tags not used in ligation reaction). The probe intensities were plotted in natural log scale on the y-axis. The horizontal dashed line is the threshold determined by analysis algorithm, which has a value of 3,800.

The array design for the experiment represented in FIG. 23 is as follows. For each gene target assayed, the array probe consists of all possible combinations of the 960 label-tag sequence and either of the two BamHI genomic fragment ends. An additional 192 label-tag sequences that were not included in the adaptor pool were also tiled to serve as non-specific controls. This tiling strategy enables consistency check on the number of label-tags used at the paired ends, since each target fragment is ligated to two independent label-tags (one on either end), and for the same target fragment, the counts on the left and right side should be very similar.

The lower panel of FIG. 23 shows the histogram of the intensity data corresponding to 960 specific label-tags. Also shown in the figure are the 2 fitted normal distributions. The fitted distributions have the mean and standard deviation of 1447±680 and 12186±3580, respectively. The vertical dashed line in the lower panel is the threshold, which has the same value as the horizontal dashed line shown in the upper panel. Based on such threshold, 501 probes (i.e., label-tags) were counted as “used”.

FIG. 24 shows the number of times observed for each of the 960 specific label-tags. Empirically, 349 label-tags were not observed in any of the 20 cases. By model, we would expect to observe 643.05±9.96 label-tags at least once, which means we expect not to observe 307327 label-tags. This result shown was obtained by grouping label-tags used in independent ligation reactions together. To more accurately estimate the frequency of usage of label-tags, only data from experiments with low concentrations (0.05 ng and 0.5 ng of DNA ligation amount) were considered. Under each concentration, 5 different gene targets independently ligated to label-tags at both ends. Therefore, a total of 20 independent reactions (2 concentrations x 5 gene targets x 2 ends) were grouped together. Of these reactions, 1,064 label-tags were observed; some were observed more often than the others, the frequency of usage of label-tags ranges from 0 to 6.

This suggests that the differential usage of label-tags may be observed before PCR is started. Such difference in the amount of molecules associated with different label-tags will carry on as PCR process goes on.

For the PCR simulations, we defined n copies of a gene fragment T, each ligated to a single counter randomly selected from an infinite pool of m unique counters to generate a collection of k resulting counter-ligated gene target molecules T*={tl_(i),i=1, 2, . . . , k}. We assumed that each counter-ligated gene target molecule tl_(i) replicates randomly and independently of other target molecules; and that the replication probability p (i.e., amplification efficiency) of different molecules, tl_(i), remains constant throughout the PCR process. For each tl_(i), we denote the number of molecules at PCR cycle c as N_(i) ^(c). When c=0, N_(i) ^(c) is the initial number of tl_(i). The PCR process at cycle c+1 can be modeled as a series of N_(i) ^(c) independent trials that determine the replicability of each of the N_(i) ^(c) molecules with replication probability p. Let ΔN_(i) ^(c) represent the number of molecules replicated at cycle c+1, then the number of molecule tl_(i) after cycle c+1 is N_(i) ^(c+1)=N_(i) ^(c)+ΔN_(i) ^(c), where the probability of ΔN_(i) ^(c) is

${p\left( {{\Delta\; N_{i}^{c}}❘N_{i}^{c}} \right)} = {\begin{pmatrix} N_{i}^{c} \\ {\Delta\; N_{i}^{c}} \end{pmatrix}{{p^{\Delta\; N_{i}^{c}}\left( {1 - p} \right)}^{N_{i}^{c} - {\Delta\; N_{i}^{c}}}.}}$ determined the relative abundance of different counter-ligated gene target molecules tl_(i) upon completion of the simulated PCR run for n=500, 50, or 5, and p=0.8, 0.7 or 0.6 (Table 5). In each case, we performed 1,000 independent runs to simulate 30 cycles of adaptor PCR, followed by 30 cycles of gene-specific PCR. Table 5 shows summary statistics drawn from 100 independent simulation runs modeling PCR, ligation at each end of targets is considered.

TABLE 5 Initial copy number N = 5 N = 50 N = 500 Side Left Right Left Right Left Right # of labels 5 5 48.61 0.99  48.64 1.09 7.18 388.91 6.85  389.27 7.18  observed Max (1.43 0.19) * (1.43 0.19) * (2.18 0.49) * (2.13 0.47) * (4.52 0.59) * (4.44 0.55) * 10{circumflex over ( )}11 10{circumflex over ( )}11 10{circumflex over ( )}10 10{circumflex over ( )}10 10{circumflex over ( )}9 10{circumflex over ( )}9 Min (5.73 2.27) * (5.73 2.27) * (2.35 1.06) * (2.35 1.06) * (1.15 0.49) * (1.23 0.49) * 10{circumflex over ( )}10 10{circumflex over ( )}10 10{circumflex over ( )}9 10{circumflex over ( )}9 10{circumflex over ( )}8 10{circumflex over ( )}8 Ratio btw 3.13 2.44 3.13 2.44 14.10 11.41 13.87 13.42 43.42 25.66 44.92 30.04 max & min Mean (1.00 0.16) * (1.00 0.16) * (1.03 0.06) * (1.03 0.06) * (1.27 0.03) * (1.27 0.03) * 10{circumflex over ( )}11 10{circumflex over ( )}11 10{circumflex over ( )}10 10{circumflex over ( )}10 10{circumflex over ( )}9 10{circumflex over ( )}9 Standard (3.44 1.02) * (3.44 1.02) * (3.98 0.52) * (3.94 0.54) * (6.75 0.41) * (6.69 0.40) * deviation 10{circumflex over ( )}10 10{circumflex over ( )}10 10{circumflex over ( )}9 10{circumflex over ( )}9 10{circumflex over ( )}8 10{circumflex over ( )}8 Coef. of 0.36 0.13 0.36 0.13 0.39 0.05 0.38 0.05 0.53 0.03 0.53 0.03 variation

Focusing on the experiments with concentrations of 0.5 and 0.05 ng, (3^(rd) and 4^(th) in each group of 5), which provide the most accurate count of label-tags, there are 20 different opportunities for a given label-tag to be observed (2 concentrations×5 amplicons×2 sides (left or right)). We observed 1,064 label-tags over the 20 opportunities.

To observe the distortion of the relative abundance of DNA molecules in the reaction resulting from the PCR process, dispersion in the quantitative distribution of PCR amplified DNA molecules was analyzed. A model of the PCR process was generated to understand the dispersion in the distribution of amplified molecules (FIG. 22, Table 6). A series of 1,000 independent simulation runs were performed to simulate the replication of 500 uniquely labeled target molecules through PCR processes. For each run, the distribution of the final amount of PCR products was determined and the dispersion of distribution was quantified using two measures: ratio of the maximal to the minimal amount, and coefficient of variation of final PCR products. For a library of 960 counters and 500 target molecules the expectation is that about 390 counters will ligate at various redundancies (1, 2, 3 and 4 are shown). For each of the 390 counters the relative ratio of its abundance to that of the counter with the lowest abundance is plotted (y-axis) for the onset of PCR (panel A), or after 5, 10 or 15 cycles of amplification (panels B-D respectively). The x-axis represents the different labeled molecules. The ratio of the most abundant to the least abundant is 30. This demonstrates that the degree of dispersion increases with the incidence of replicate use of identical counters, which may be in-part responsible for the deviation observed when assaying high target copy numbers. Table 6 lists the ratio and CV for distributions corresponding to different concentrations and replication probabilities (one sided ligation considered).

TABLE 6 replication probability n = 5 n = 50 n = 500 Ratio of max to min p = 0.6 5.69 ± 4.95 26.16 ± 23.78 124.18 ± 88.04  amount of PCR p = 0.7 4.59 ± 8.03 16.22 ± 15.53 71.55 ± 55.13 amplified product p = 0.8 2.82 ± 1.51 11.54 ± 9.53  42.24 ± 27.49 Coefficient of p = 0.6 0.48 ± 0.16 0.51 ± 0.06 0.62 ± 0.03 Variation (CV) p = 0.7 0.41 ± 0.14 0.44 ± 0.05 0.57 ± 0.02 p = 0.8 0.34 ± 0.12 0.36 ± 0.05 0.52 ± 0.02

Example 1 of a method for selecting a collection of label-tags starting with all possible 14 mers (4¹⁴ or ˜268 million possible label-tags). Step 1: clustering based on the last 7 bases: all sequences with the same last 7 bases are grouped together; within each cluster, randomly pick one sequence, this gives us 11,025 sequences, denoted by set A. Step 2: clustering based on the first 7 bases: all sequences with the same first 7 bases are grouped together; within each cluster, randomly pick one sequence, this gives us 13,377 sequences, denoted by set B. Step 3: get the union set of set A and B, the combined set has 24,073 sequences. Then do clustering based on the middle 6 bases, randomly pick one sequence out of every cluster, this gives us 3,084 sequences, denoted by set C. Step 4: calculate the all-against-all alignment score of set C, which gives us a 3,084×3,084 self-similarity score matrix, denoted by S. Step 5: filter based on the score matrix. If an element of the score matrix S(i,j) has a high value, that means, the corresponding sequences i and j are very similar to each other. Starting from the elements with top self-similarity score, randomly pick one and discard the other; repeat this process until the number of retained sequences <2000. Until this step, 1,927 sequences were retained.

For the retained 1,927 sequences, an all-against-all complement score was calculated for each. This gave a 1,927×1,927 cross complement score matrix. A step similar to step 5 was performed, to avoid label-tags with maximal cross-complement with other label-tags. Starting from the pairs with top cross-complement score, one was randomly pick and the other discarded. This process was repeated until the number of retained sequences was 1920. Next the 1920 label-tags were split into 2 sets, with one set (denoted by set A) consisting of sequences that are maximum different from one-another; and the other set (denoted by set B) consisting of the remaining sequences. The procedure used to split sequences was as follows. Starting from the original 1920 by 1920 similarity score matrix, for each sequence, first, sum up all its similarity scores with the rest of the sequences in the pool, that is, for each sequence, calculate a total similarity score. Second, sort the total similarity scores of all sequences and select the sequence with the lowest total score, and move it to set A. Third, remove the row and column corresponding to the selected sequence, i.e., both the number of rows and columns in the similarity score matrix are reduced by 1. Repeat steps 1-3, until the number of rows and columns in the similarity score matrix reaches 960 or half of the original. The selected sequences belong to set A and the remaining sequences belong to set B.

In another embodiment a collection of label-tags is selected using the following steps. Starting with all possible 14 mers (4¹⁴ or ˜268 million possible label-tags) eliminate all that do not have 50% GC content. Eliminate those were each nucleotide does not occur at least twice. Eliminate those that have more than two G/C in tandem or more than three A/T in tandem. Eliminate those that contain a selected restriction site. That reduces the original set to ˜33 million or 12.43% of the original set. From that set select those that have a Tm within the range of 38.5° C. to 39.5° C. This step results in a set of ˜7 million or 2.73% of the original set. Remove those that have regions of self-complementarity. The resulting set in this example was now 521,291. A hierarchical clustering was performed to identify a set that has maximum sequence difference between one-another. The resulting set contained 1,927 label-tags. Label-tags were removed if the sequence had a tendency to bind to other label-tags in the set. This reduced the set to 1,920 label-tags. A final set of 960 label-tags was selected from the 1,920 as being maximally different for the “specific” label-tags and 192 additional counters to tile on the array as “non-specific” controls.

Selection of Targets and design of test array. Regions selected to assay as targets included Chr X, Chr Y, Chr 4 as a reference and Chr 21 for Trisomy. Locations on the chromosomes for assaying were selected to avoid centromeres and telomeres. Fragments were selected based on Bam HI fragments of between about 400 and 600 base pairs. Fragment intensity was checked using HG49 array hybridization. The first and the last 26 nucleotides of the fragments (from and including the Bam HI site) were tiled. Repeats were avoided and GC % was optimized.

The array format was 100/25. Feature size is Sum. There are 436×436 features or 190,096 features. Synthesis was NNPOC, 43 mer probes, 5′ up, no phosphate. The chip name is STCL-test2. The gridding probe used was the same as the HG49. No quality control probes were included.

Aside from reducing whole chromosomes into 360,679 smaller molecular weight DNA pieces more suitable for ligation reactions, restriction digestion also serves to reduce the overall sequence complexity of the sample, as only an estimated 79,517 fragments reside in the 150 bp-2 kb size range that is effectively amplified by PCR. To detect and quantify counters that have been selected by the target molecules, the labeled genomic target fragments may be circularized and PCR amplified to prepare for analysis, for example, using microarray hybridization or DNA sequencing. A representative BamHI target fragment was sampled for each of the three test chromosomes. Simultaneous measurements of all three chromosomes serve as an internal control independent of dilution or other systematic errors. A suitable DNA array detector capable of distinguishing the set of counters bound to copies of the target molecules was constructed using photolithography (S. P. Fodor et al., Science 251, 767 (Feb. 15, 1991). Each array element for a target to be evaluated consists of a target complementary sequence adjacent to one of the complements to the 960 counter sequences. For increased specificity, a ligation-readout was performed on the microarray after hybridization to avoid false positive detection of the cross-hybridization of identical targets with different counters. As a means of validation through a secondary measure, samples hybridized to microarrays were subsequently sampled by DNA sequencing (FIGS. 10 and 25).

An equation to model the stochastic labeling of target molecules with a small library of 960 counters, and validate our equation model with numerical simulations is disclosed. In the model, the diversity of counters selected by, and ligated to target molecules in the reaction solution (simplified as ‘used’) is dictated by the number of copies of molecules present for each target fragment in the reaction (FIG. 12). Under conditions where the size of the counter library is much greater than the number of copies of a given target molecule, the counting efficiency is high, and counting the number of counters used is equivalent to counting the number of copies of the original target molecules (FIG. 16). When the number of target copies approaches and exceeds the number of different counters in the reaction, any counter in the library is more likely to be used multiple times (FIG. 15). The number of counters used at least once is an important measure because it serves as the basis for drawing yes/no conclusions in our digital readout on microarrays. Under stochastic labeling conditions, we expect that the absolute quantity of single DNA molecules can be accurately determined by proxy counts of labeling events. Indeed, microarray experiments demonstrate a high degree of correlation between the number of copies of target molecules added to the reaction and the number of counters used, as detected on microarrays (FIG. 12). In particular, counter usage precisely profiles the number of target molecules under conditions of high counting efficiency. Subtle deviations from the model may represent minor dilution errors in the preparation of the sample. However, within that sample dilution, the relative counter ratios of the three internally built-in controls are highly accurate (FIG. 13). FIG. 13 shows comparison of relative copy ratios of the three gene targets tested: ChrX, Chr4 and Chr21 representing genetic material of one, two and three copies per cell. Different dilutions (5 ng, 2 ng, 0.5 ng and 0.05 ng) of a DNA sample isolated from cultured lymphoblasts of a Trisomy 21 male individual were processed for microarray hybridization and DNA sequencing. The calculated number of target molecules (see, Table 4, column 9) was inferred from the number of counters detected on microarrays (A), and was also calculated for the SOLID sequencing data (B). For each sample dilution, the target copy number ratio of each gene target relative to ChrX is shown.

On the other hand, when target copies exceed ˜100, detected labeling events appear to indicate fewer than actual molecules in solution (FIG. 12 inset in graph on left). This deviation was reproducible and consistently observed across multiple microarray experiments, and was also observed in the DNA sequencing experiments (FIG. 12 inset in graph on right). Under-counts of expected labeling events may originate from inadequate detection sensitivity of the microarray platform or from other systematic or indeterminate deficiencies in the sample preparation procedure. PCR, for example, is prone to amplification bias (T. Kanagawa, J Biosci Bioeng 96, 317 (2003) and M. F. Polz, C. M. Cavanaugh, Appl Environ Microbiol 64, 3724 (1998)), which could hinder the comprehensive detection of labeling events that may be genuinely stochastic.

To confirm the microarray results, a digital sequence counting of individual molecules in the DNA samples hybridized to microarrays was used as a means of validation, and to detect the presence of any false negatives that may have escaped microarray detection. Analysis of mapped sequence reads resulted in counts in agreement to the microarray observations. Furthermore, a second, independent sequencing run was repeated with similar findings (Table 3).

An additional feature of digital sequence counting is that unlike the microarray intensity data (FIGS. 20 and 21), which may provide lower resolution into the measurement of the concentration dispersion of PCR amplified molecules, sequence counting clearly demonstrates significant variation in the representation of amplified targets (FIG. 25), This is consistent with the computed PCR model. Overall, detected counters on the microarray and sequencing experiments correlate well, but a small subset of counters appear to be unique to each process (Table 7). The observed number of label-tags in common between the microarray and the two sets of sequencing experiments are summarized in the table. The number of label-tags in each category is included. The categories are as follows: A+1+2 for label-tags detected in each of the 3 experiments, 1+2 for label-tags detected only in sequencing runs 1 and 2, 1+A for label-tags detected in sequencing run 1 and by array, and so on for the amounts of DNA shown in column 3.

TABLE 7 A + 1 + 1 + DNA sample 1 + 2 2 A 2 + A 1 2 A Chr4 Left side 0.036 ng  13 0 0 0 0 0 1 0.36 ng 96 3 0 1 2 2 5 1.45 ng 228 13 4 22 6 10 6 3.62 ng 484 23 2 3 4 6 12 Right side 0.036 ng  14 0 0 0 0 0 0 0.36 ng 100 1 0 0 2 2 7 1.45 ng 249 25 2 0 15 33 5 3.62 ng 511 22 2 1 9 23 11 Chr21 Left side 0.036 ng  18 0 2 0 0 0 0 0.36 ng 150 0 2 4 0 7 4 1.45 ng 324 17 8 1 32 16 2 3.62 ng 637 14 10 0 17 14 4 Right side 0.05 ng 18 0 1 1 0 0 0 0.36 ng 144 0 2 2 0 0 9 1.45 ng 330 34 2 3 15 12 6 3.62 ng 615 29 1 7 5 2 4 ChrX Left side 0.036 ng  11 0 0 0 0 0 0 0.36 ng 42 0 0 0 1 3 8 1.45 ng 137 3 1 5 8 5 5 3.62 ng 274 12 0 2 4 12 5 Right side 0.036 ng  10 1 0 0 1 0 0 0.36 ng 43 0 3 0 4 0 2 1.45 ng 127 15 0 0 11 25 6 3.62 ng 298 12 3 3 24 31 2

For the reverse scenario, high numbers of mapped sequence reads were always observed to correlate with high microarray intensities in these examples. No systematic or sequence correlations, or explanations were identified for the counters that are absent from any given sequencing experiment for which the microarray readout demonstrates a strong signal. While obviously underrepresented in some experiments, the same counters are sometimes present in high sequence counts in other experiments, suggesting that they are available for sequencing. PCR was used to resolve these isolated cases of disagreement and demonstrate these were false negatives in the sequencing experiments (Table 3). Despite their presence in the sequencing library, it is unclear why the counters were not observed or were underrepresented in the original sequencing run, and also in the subsequent replicate sequencing run.

Aside from the comparative analysis of absolute and relative counts of the numbers of target molecules and counter label-tags, additional ways to assess the stochasticity of the labeling process were evaluated. First, if the labeling process is random, the frequency of incorporation of identical counters in independent events across the paired left and right termini of target fragments should closely resemble outcomes from numerical simulation. Observed counts on microarrays do in fact match closely with numbers obtained from computer simulations (Table 4, columns 10-11). Second, if the target molecules are labeled randomly with an equal likelihood of incorporation for any member of the 960 counters in the library, we would expect the number of repeated observations of counters to follow a stochastic nature. For this analysis, we accumulated a total of 1,064 counter observations over several microarray experiments restricted to low target copy numbers. Exclusion of data from high copy targets was necessary to avoid undercounting labeling events from multiple incidences of identical counters attaching individually to numerous target copies. As a further and final demonstration of stochastic labeling, results show that the frequency of label-tag usage follows a pattern consistent with outcomes from numerical simulation.

Having now fully described the present invention in some detail by way of illustration and example for purposes of clarity of understanding, it will be obvious to one of ordinary skill in the art that the same can be performed by modifying or changing the invention within a wide and equivalent range of conditions, formulations and other parameters without affecting the scope of the invention or any specific embodiment thereof, and that such modifications or changes are intended to be encompassed within the scope of the appended claims.

All publications, patents and patent applications mentioned in this specification are indicative of the level of skill of those skilled in the art to which this invention pertains, and are herein incorporated by reference to the same extent as if each individual publication, patent or patent application was specifically and individually indicated to be incorporated by reference. 

We claim:
 1. A method comprising: a) attaching a plurality of diverse label-tags to a nucleic acid target from a sample that contains multiple copies of the nucleic acid target, thereby producing a plurality of labeled targets, wherein: i) a label-tag of the plurality of diverse label-tags comprises nucleotides selected from purine bases, pyrimidine bases, natural nucleotide bases, chemically modified nucleotide bases, biochemically modified nucleotide bases, non-natural nucleotide bases; and ii) a labeled target of the plurality of labeled targets comprises a distinct label-tag and at least a portion of a nucleic acid target, or its complementary sequence; b) amplifying the plurality of labeled-targets to produce a plurality of amplified labeled-targets, wherein an amplified labeled-target of the plurality of amplified labeled-targets comprises a copy of at least a portion of the nucleic acid target, or its complementary sequence, and a copy of the label-tag; and c) detecting the plurality of amplified labeled-targets by sequencing at least a portion of the target and the label-tag; and d) determining the number of copies of the nucleic acid target, as indicated by the number of different label-tags that are associated with the nucleic acid target.
 2. The method of claim 1, wherein the label-tag comprises at least 8 nucleotides, wherein each of the at least 8 nucleotides are selected from the group consisting of purine bases, pyrimidine bases, natural nucleotide bases, chemically modified nucleotide bases, biochemically modified nucleotide bases, and non-natural nucleotide bases.
 3. The method of claim 2, wherein the label-tag comprises from at least 2 to at least 20 nucleotides, wherein each of nucleotides are selected from the group consisting of purine bases, pyrimidine bases, natural nucleotide bases, chemically modified nucleotide bases, biochemically modified nucleotide bases, and non-natural nucleotide bases.
 4. The method of claim 1, wherein the label-tag further comprises a universal primer sequence.
 5. The method of claim 4, wherein amplifying comprises use of primers that bind to the universal primer sequence of the label-tag.
 6. The method of claim 1, wherein the amplifying comprises polymerase chain reaction (PCR).
 7. The method of claim 6, wherein PCR comprises balanced PCR.
 8. The method of claim 6, wherein PCR comprises rolling circle amplification.
 9. The method of claim 1, wherein the nucleic acid target is DNA.
 10. The method of claim 1, wherein the nucleic acid target is RNA.
 11. The method of claim 1, further comprising enriching the sample for the nucleic acid target.
 12. The method of claim 1, wherein the sample comprises polynucleotides from tumor cells.
 13. The method of claim 1, wherein the sample comprises polynucleotides from bacteria.
 14. The method of claim 1, wherein the attaching step comprises ligating the plurality of label-tags to the multiple copies of the nucleic acid target.
 15. The method of claim 1, wherein the attaching step comprises primer extension of the plurality of label-tags hybridized to the multiple copies of the nucleic acid target.
 16. The method of claim 1, wherein the attaching step occurs on both ends of the nucleic acid target.
 17. The method of claim 1, wherein the attaching step occurs in a stochastic manner.
 18. The method of claim 1, wherein the attaching step occurs in a sequence independent manner.
 19. The method of claim 1, wherein the sample is from a human subject.
 20. The method of claim 19, wherein the sample comprises polynucleotides from tumor cells.
 21. The method of claim 1, wherein the nucleic acid target comprises fragmented nucleic acids. 